Statistics Questions

Using the following uniform density curve answer the question P x 125 1 What is the probability that the random variable has a value less than 2 5 2 What is the probability that the random variable has a value between 0 2 and 0 8

The probability that an individual has 20 20 vision is 0 14 In a class of 32 students what is the probability of finding five people with 20 20 vision O 0 14 O 0 156 O 0 925 O 0 185

5 Find the area of the shaded region The graph depicts the standard normal distribution with mean 0 and standard deviation 1 6 3 39 2 26 1 13 1 84 0 92 1 13 2 26 3 39 Z 0 92 1 84 Area Area

Use the discrete probability distribution below to find the probability that x equals 4 4 7 9 0 18 0 03 x P x 3 0 15 O 0 61 O2 56 O 0 1521 O 0 64

Assume that the weight loss for the first month of a diet program varies between 6 pounds and 12 pounds and is spread evenly over the range of possibilities so that there is a uniform distribution Find the probability of the given range of pounds lost 3 Less than 11 pounds 4 Between 8 5 pounds and 10 pounds

Suppose your city has a large hospital and a small hospital each performing major and minor surgeries You collect data to see how many surgical patients have their discharges delayed by postsurgical complications and find the results shown in the table a Overall for what percent of patients was discharge delayed Round to one decimal place as needed Major Minor Large 115 of 85 10 of 40

ANSWER Write the word or phrase that best completes each statement or answers the question Find the indicated probability Round to three decimal places 18 A test consists of 10 true false questions To pass the test a student must answer at least 6 questions correctly If a student guesses on each question what is the probability that the student will pass the test 18 4 I MULTIPLE CHOICE Choose the one alternative that best completes the statement or answers the question 19 Find the probability of at least 2 girls in 7 births Assume that male and female births are equally likely and that the birthe ara indonondont quanto

Solve the problem 24 According to a college survey 22 of all students work full time Find the standard deviation for the number of students who work full time in samples of size 16 24 A 2 6 B 1 9 C 1 7 D 3 5 Determine if the outcome is unusual Consider as unusual any result that differs from the mean by more than 2 standard deviations That is unusual values are either less than 20 or greater than u 20 25 A survey for brand recognition is done and it is determined that 68 of consumers have heard of Dull Computer Company A survey of 800 randomly selected consumers is to be conducted For such groups of 800 would it be unusual to get 634 consumers who recognize the Dull Computer Company name 25 A Yes B No 26 A survey for brand recognition is done and it is determined that 68 of consumers have heard of Dull Computer Company A survey of 800 randomly selected consumers is to be conducted For such groups of 800 would it be unusual to get 530 consumers who recognize the Dull Computer Company name 26

7 A police department reports that the probabilities that 0 1 2 and 3 burglaries will be reported in a given day are 0 53 0 43 0 03 and 0 01 respectively 7 A 0 25 B 1 05 Provide an appropriate response Round to the nearest hundredth 8 Find the standard deviation for the given probability distribution x P x 0 0 12 1 0 07 2 0 21 3 0 30 4 0 30 A 1 35 C 1 50 D 0 52 B 2 90 C 1 30 D 1 70 8

0 183 0 311 0 264 0 150 and 0 064 respectively MULTIPLE CHOICE Choose the one alternative that best completes the statement or answers the question Find the mean of the given probability distribution 6 In a certain town 40 of adults have a college degree The accompanying table describes the probability distribution for the number of adults among 4 randomly selected adults who have a college degree X P x 0 0 1296 1 0 3456 2 0 3456 30 1536 4 0 0256 6

Consider a set of data in which the sample mean is 33 7 and the sample standard deviation is 7 2 Calculate the z score given that x 30 2 Round your answer t two decimal places

A Assume you are doing some research What question would you like to ask your peers at IRSC Describe how you will collect your data and describe what a sampling error AND also a non sampling errror might be with your research

2 2 2 4 Quiz Population Genetics Number of students 18 16 14 12 10 8 6 4 2 0 Heights of Male Students 158 165 166 173 174 181 182 189 190 197 Height cm Which range of heights represents the tallest 8 of 17 year old male students

According to the American Time Use Survey Americans age 15 and over spend an average of 2 69 hours each day watching television Assume the distribution of all such amounts of time spent watching television is normally distributed with a standard deviation of 1 15 hours Use this information to determine the following two probabilities Round solutions to four decimal places if necessary Find the probability that a single randomly American age 15 and over watches television more than 2 62 hours per day P x 2 62 Find the probability that the mean time spent watching television per day of a random sample of 47 Americans age 15 and over is more than 2 62 hours P Z 2 62

Suppose that 43 of voters in St Lucie county support a proposed zoning ordinance Consider the sampling distribution of the sample proportion of supporters with sample size n 125 Determine the mean and standard deviation of the sampling distribution of p Round solutions to four decimal places if necessary What is the mean of this distribution Hp What is the standard error of this distribution M

Suppose that IQ scores have a bell shaped distribution with a mean of 97 and a standard deviation of 17 Using the empirical rule what percentage of IQ scores are at least 46 Please do not round your answer

Based on a survey assume that 34 of consumers are comfortable having drones deliver their purchases Suppose that we want to find the probability that when four consumers are randomly selected exactly two of them are comfortable with delivery by drones Identify the values of n x p and q The value of n is Type an integer or a decimal Do not round The value of x is Type an integer or a decimal Do not round The value of p is Type an integer or a decimal Do not round The value of q is Type an integer or a decimal Do not round ACEED

the following 9 13 14 14 9 14 9 1 of 3 Calculate the value of the sample variance Round your answer to one decimal place

t has become more common for shoppers to comparison shop using the Internet Respondents to a survey who owned cell phones were asked whether they had in the past 30 days looked up the price of a product while they were in a store to see if they could get a better price somewhere else The table to the right has their responses by income level Complete parts a through d below Yes No 30K 30K 49 9K 205 110 619 415 a Find the conditional distribution in percentages of income distribution for those who do not compare prices on the Internet 30K 30K 49 9K 50K 74 9K 50K 74 9K 129 252 75K 208 426 Not Comparing

According to the Martin Economic Development Council the average household income in Martin county is 46 825 with a standard deviation of 2 910 Determine the following probabilities Round solutions to four decimal places if necessary Determine the probability that a randomly selected Martin county household has an income greater than or equal to 42 393 P r 42 393 Determine the probability that a randomly selected Martin county household has an income between 39 388 and 42 209 P 39 388 x 42 209

Find the area under the standard normal curve within 1 7 standard deviations of the mean Round the solution to four decimal places if necessary Area

Leta be a normally distributed continuous random variable with a mean of 291 and a standard deviation of 26 Determine the value of a such that the area to the left of x is 0 2743 Round the solution to two decimal places if necessary 89 11

What does the notation Za indicate The expression za denotes the z score with an area of a

Based on the Consumer Transportation Survey data below develop a probability mass function and cumulative distribution function both tabular and as charts for the random variable number of children a What is the probability that an individual in this survey has fewer than three children b What is the probability that an individual in this survey has at least one child c What is the probability that an individual in this survey has five or more children Click the icon to view the Consumer Transportation Survey data Develop a probability mass function table X 0 1 2 Round to three decimal places as needed 3 4 5 or more B D 1ehicle Drivel Type stisfaction with vehicGender 2 Truck Domestic Yes Foreign No 3 Truck 4 Truck Male Male Male Male Domestic No Domestic Yes 5 SUV 6 SUV Domestic No 7 SUV Domestic No 8 SUV 9 SUV 10 SUV 11 SUV 12 SUV 13 Mini Van 14 Mini Van 15 Mini Van 16 Mini Van 17 Mini Van 18 Car 19 Car 20 C 21 Car 22 Car 23 Car 24 Car 25 Car 26 Car 27 Car 28 Ca 29 Car 30 Car 31 Car 32 33 34 Domestic Yes Domestic Yes Foreign Yes Domestic Yes Foreign Yes Domestic Yes Foreign Yes Domestic No Foreign Yes Domestic No Dornestic Yes Domestic Yes Domestic Yes Foreign Yes Domestic Yes Foreign No Foreign Yes Domestic No Domestic Yes Foreign Yes Domestic No Domestic No Domestic Yes Foreign No Female Female Male Male Male Male Male Female Female Female Female Male Fernale Female Female Female Female Female Male Male Female Male Male Female Female Female E F G H Age of hours per week in vehililes drive per wecumber of Childreerage number of rideMiles from work 29 26 18 31 31 29 28 49 50 48 45 33 28 B 43 38 35 39 51 22 34 47 19 33 46 21 30 44 62 29 42 12 6 10 15 4 21 16 15 51 10 8 201 10 5 10 11 5 10 4 5 15 4 Al 5t 6 51 51 51 3701 580 300 675 800 300 400 1000 840 1400 300 800 350 7000 450 350 700 600 250 600 300 500 400 275 150 351 285 175 250 400 0 of 2 21 0 0 0 0 11 4 4 1 15 201 35 50 20 151 22 45 25 201 51 0 0 0 0 45 40 3 16 21 4 22 18 n 18 16 0 19 22

What conditions would produce a negative z score Choose the correct answer below A a z score corresponding to a value located to the right of the mean OB an area in the top 10 of the graph OC a z score corresponding to a value located to the left of the mean D a z score corresponding to a negative area

2 Construct a truth table for the statement q V pVq pv q P 9 9 8 pts qV pVq

Identify the margin of error 211 8 dollars Round to one decimal place as needed Construct a 95 confidence interval for the population mean Part 2 of 3 Round to one decimal place as needed Points 0 4 of 1 In a random sample of seven cell phones the mean full retail price was 591 50 and the standard deviation was 229 00 Assume the population is normally distributed and use the t distribution to find the margin of error and construct a 95 confidence interval for the population mean Interpret the results Save

The monthly incomes for 12 randomly selected people each with a bachelor s degree in economics are shown on the right Complete parts a through c below Assume the population is normally distributed a Find the sample mean x 4263 1 Round to one decimal place as needed b Find the sample standard deviation S Round to one decimal place as needed 4450 31 4455 08 4283 49 3946 76 4596 4151 452 402

Part 1 of 3 O Points 0 A researcher wishes to estimate with 99 confidence the population proportion of adults who support labeling legislation for genetically modi the true proportion a No preliminary estimate is available Find the minimum sample size needed b Find the minimum sample size needed using a prior study that found that 77 of the respondents said they support labeling legislation fa c Compare the results from parts a and b a What is the minimum sample size needed assuming that no prior information is available n Round up to the nearest whole number as needed

Choose the correct answer below OA If the distribution of the sample means is normally distributed and n 30 then the population distribution normally distributed OB If the original population is not normally distributed and n 30 the distribution of the sample means can b approximated reasonably well by a normal distribution OC The distribution of sample means gets closer to a normal distribution as the sample size n gets larger OD If the original population is normally distributed then for any sample size n the sample means will be nor distributed

A cheese processing company wants to estimate the mean cholesterol content of all one ounce servings of a type of cheese The estimate must be within 0 66 milligram of the population mean a Determine the minimum sample size required to construct a 95 confidence interval for the population mean Assume the population standard deviation is 3 17 milligrams b The sample mean is 25 milligrams Using the minimum sample size with a 95 level of confidence does it seem likely that the population mean could be within 3 of the sample mean within 0 3 sample mean Explain Click here to view page 1 of the Standard Normal Table Click here view page 2 of the Standard Normal Table a The minimum sample size required to construct a 95 confidence interval is Round up to the nearest whole number Standard Normal Table Page 2 servings 0 3 0 4 0 5 0 6 0 7 GALE 4 Z 0 06 0 08 0 07 0 09 0 04 0 05 0 03 0 02 0 01 0 00 0 0 0 5000 0 5040 0 5080 0 5120 0 5160 0 5199 0 5239 0 5279 0 5319 0 5359 0 1 0 5398 0 5438 0 5478 0 5517 0 5557 0 5596 0 5636 0 5675 0 5714 0 5753 0 2 0 5793 0 5832 0 5871 0 5910 0 5948 0 5987 0 6026 0 6064 0 6103 0 6141 0 6179 0 6217 0 6255 0 6293 0 6331 0 6368 0 6406 0 6443 0 6480 0 6517 0 6554 0 6591 0 6628 0 6664 0 6700 0 6736 0 6772 0 6808 0 6844 0 6879 0 6915 0 6950 0 6985 0 7019 0 7054 0 7088 0 7123 0 7157 0 7190 0 7224 0 7257 0 7291 0 7324 0 7357 0 7389 0 7422 0 7454 0 7486 0 7517 0 7549 0 7580 0 7611 0 7642 0 7673 0 7704 0 7734 0 7764 0 7794 0 7823 0 7852 0 8 0 7881 0 7910 0 7939 0 7967 0 7995 0 8023 0 8051 0 8078 0 8106 0 8133 0 9 0 8159 0 8186 0 8212 0 8238 0 8264 0 8289 0 8315 0 8340 0 8365 0 8389 8138 0 8461 0 8485 0 8508 0 8531 0 8554 0 8577 0 8599 0 8621 0770 0 8790 0 8810 0 8830 X

The standard deviation of the distribution of sample means is The standard deviation of the distribution of sample means is O

A genetics experiment involves a population of fruit flies consisting of 3 males named Alfonso Barry and Carlos and 1 female named Diane Assume that two fruit flies are randomly selected with replacement a After listing the possible samples and finding the proportion of females in each sample use a table to describe the sampling distribution of the proportion of females Proportion of females Probability 0 0 5 Type integers or fractions

K Use the given confidence interval to find the margin of error and the sample proportion 0 609 0 637 E 0 014 Type an integer or a decimal p Type an integer or a decimal

K You are given the sample mean and the population standard deviation Use this information to construct the 90 and 95 confidence intervals for the population mean Interpret the results and compare the widths of the confidence intervals From a random sample of 65 dates the mean record high daily temperature in a certain city has a mean of 85 21 F Assume the population standard deviation is 13 70 F The 90 confidence interval is 82 41 88 01 Round to two decimal places as needed The 95 confidence interval is 81 88 88 54 Round to two decimal places as needed Which interval is wider Choose the correct answer below Save O The 90 confidence interval O The 95 confidence interval

Part 2 of 3 a Find the sample mean x 2 32 Round to two decimal places as needed b Find the sample standard deviation S Round to two decimal places as needed The grade point averages GPA for 12 randomly selected college students are shown on the right Complete parts a through c below Assume the population is normally distributed Ints U of NIN 2 2 1 7 2 3 0 3 5551 MOT 3 5 0 5 1 5 2 1 2 70 4 0 3 6 3 4 243

Part 1 of 3 10 A publisher wants to estimate the mean length of time in minutes all adults spend reading newspapers To determine this estimate the publisher takes a random sample of 15 people and obtains the results below From past studies the publisher assumes o is 1 9 minutes and that the population of times is normally distributed 12 8 7 7 8 6 6 11 Points 0 of 1 10 12 9 Construct the 90 and 99 confidence intervals for the population mean Which interval is wider If convenient use technology to construct the confidence intervals The 90 confidence interval is Round to one decimal place as needed 11 Save 8 8

The t value of t Round to two decima In a sample of 13 randomly selected high school seniors the mean score on a standardized test was 1187 and the standard deviation was 164 4 Further research suggests that the population mean score on this test for high school seniors is 1029 Does the t value for the original sample fall between to 90 and to go Assume that the population of test scores for high school seniors is normally distributed fall between to 90 and to 90 because to 90 does not Points 0 of 1 1 21 Save

Without doing any computation decide which has a higher probability assuming each sample is from a population that is normally distributed with 100 and o 15 Explain your reasoning a P 90 x 110 for a random sample of size n 10 b P 90 x 110 for a random sample of size n 20 Choose the correct answer below GO OA P 90 x 110 for a random sample of size n 10 has a higher probability As n increases the standard deviation decreases OB P 90 x 110 for a random sample of size n 10 has a higher probability As n increases the standard deviation increases OC P 90 x 110 for a random sample of size n 20 has a higher probability As n increases the standard deviation decreases OD P 90 x 110 for a random sample of size n 20 has a higher probability As n increases the standard deviation increases

Determine and d H 67 from the given parameters of the population and sample size 67 o 21 n 20 Round to three decimal places as needed

The 95 confidence interval for the population mean u is Round to two decimal places as needed Part 1 of 3 0 0 Points 0 of 1 In a random sample of five mobile devices the mean repair cost was 70 00 and the standard deviation was 13 00 Assume the population is normally distributed and use a t distribution to find the margin of error and construct a 95 confidence interval for the population mean Interpret the results Save

Use the standard normal distribution or the t distribution to construct a 99 confidence interval for the population mean Justify your decision If neither distribution can be used explain why Interpret th in a random sample of 42 people the mean body mass index BMI was 29 1 and the standard deviation was 6 12 Which distribution should be used to construct the confidence interval Choose the correct answer below A Use a normal distribution because the sample is random na 30 and a is known B Use a t distribution because the sample is random na 30 anda is unknown OC Use a normal distribution because the sample is random the population is normal and a is known D Use a t distribution because the sample is random the population is normal and a is unknown E Neither a normal distribution nor a t distribution can be used because either the sample is not random or n 30 and the population is not known to be normal Select the correct choice below and if necessary fill in any answer boxes to complete your choice OA The 99 confidence interval is Round to two decimal places as needed OB Neither distribution can be used to construct the confidence interval

Suppose a simple random sample of size n 36 is obtained from a population with 82 and o 6 a Describe the sampling distribution of x b What is P x 83 c What is P x 80 d What is P 81 45 x 83 6 Click here to view the standard normal distribution table page 1 Click here to view the standard normal distribution table page 2 a Choose the correct description of the shape of the sampling distribution of x O A The distribution is approximately normal OB The distribution is skewed right OC The distribution is uniform OD The distribution is skewed left OE The shape of the distribution is unknown

A simple random sample of size n 60 is obtained from a population with 69 and o 9 Does the population need to be normally distributed for the sampling distribution of x to be approximately normally distributed Why What is the sampling distribution of x Does the population need to be normally distributed for the sampling distribution of x to be approximately mormally distributed Why OA No because the Central Limit Theorem states that regardless of the shape of the underlying population the sampling distribution of x becomes approximately normal as the sample size n increases OB Yes because the Central Limit Theorem states that only for underlying populations that are normal is the shape of the sampling distribution of x normal regardless of the sample size n OC No because the Central Limit Theorem states that only if the shape of the underlying population is normal or uniform does the sampling distribution of x become approximately normal as the sample size n increases OD Yes because the Central Limit Theorem states that the sampling variability of nonnormal populations will increase as the sample size increases

Determine and o from the given parameters of the population and sample size 67 o 21 n 20

In a random sample of seven cell phones the mean full retail price was 591 50 and the standard deviation was 229 00 Assume the population is normally distributed and use the t distribution to find the margin of error and construct a 95 confidence interval for the population mean Interpret the results Identify the margin of error Ro dollars square dollars cell phones is needed

K Use the confidence interval to find the estimated margin of error Then find the sample mean A biologist reports a confidence interval of 2 4 3 8 when estimating the mean height in centimeters of a sample of seedlings The estimated margin of error is CELE

Construct the confidence interval for the population mean c 0 90 x 9 9 o 0 7 and n 58 A 90 confidence interval for is Round to two decimal places as needed

K Find the critical value z necessary to form a confidence interval at the level of confidence shown below C 0 86 Zc Round to two decimal places as needed

Suppose that grade point averages of undergraduate students at one university have a bell shaped distribution with a mean of 2 62 and a standard deviation of 0 4 Using the empirical rule what percentage of the students have grade point averages that are less than 3 82 Please do not round your answer