Statistics Questions

The probability distribution for the random variable x follows X 20 0 25 25 0 15 30 0 20 35 0 40 a Is this probability distribution valid Explain Since f x O for all values of x and f x b What is the probability that x 30 c What is the probability that x is less than or equal to 25 d What is the probability that x is greater than 30 this Select roper probability distribution is not

Step 1 a Compute E x the expected value of x The expected value of a random variable is a measure for the central location Thus the expected value of a random variable is another way to refer to the mean Recall the formula the expected value E x of a discrete random variable x Multiply each value of the random variable by its respective probability and then sum these values xf x It can be helpful to add a column to the given table of information to organize the products of xf x Complete the table X 4 E x 8 f x 0 25 0 50 12 0 25 Thus E x A xf x 4 0 25 E x xf x

300 400 400 500 Unit Demand Probability X f x 500 600 Here the random variable x is represented by the unit demand 600 Step 2 The random variable x in this distribution is represented by the unit demand column and the probability f x in this distribution is represented by the probability column Complete the table by multiplying each value of the random variable by its respective probability The expected value will be the sum of these values 0 35 0 15 0 15 0 30 0 30 0 20 0 20 xf x 300 0 35 E x xf x Therefore the monthly order should be unit demand column and f x is represented by the probability units probability column

The following table provides a probability distribution for the random variable y y f y 2 0 30 7 0 10 0 40 8 0 20 a Compute E y E y b Compute Var y and a Round your answer for a to two decimal places Var y

New legislation passed in 2017 by the U S Congress changed tax laws that affect how many people file their taxes in 2018 and beyond These tax law changes will likely lead many people to seek advice from their accountants An accounting firm in New York state believes that it may have to hire additional accountants to assist with the increased demand in tax advice for the upcoming t season The firm has developed the following probability distribution for x number of new clients seeking tax advice X f x 20 0 05 25 0 20 30 0 30 35 0 15 40 0 10 45 0 10 50 0 10 a Is this a valid probability distribution Explain This probability distribution Select valid because Select for all values of x Also f x b What is the probability that the firm will obtain 40 or more new clients c What is the probability that the firm will obtain fewer than 35 new clients d Compute the expected value variance and standard deviation of x Round your answers to four decimal places expected value variance

A psychologist determined that the number of sessions required to obtain the trust of a new patient is either 1 2 or 3 Let x be a random variable indicating the number of sessions rec the patient s trust The following probability function has been proposed for x 1 2 or 3 f x a Is this probability function valid Explain This probability distribution Select valid because Select for x 1 2 3 Also f x b What is the probability that it takes exactly 2 sessions to gain the patient s trust Round your answer to three decimal places c What is the probability that it takes at least 2 sessions to gain the patient s trust Round your answer to three decimal places

2 I surveyed each house on the block to determine how much we are spending on Halloween treats The distribution below represents the results in dollars Spent mid 50 59 54 5 40 49 44 5 30 39 34 5 20 29 24 5 10 19 14 5 0 9 4 5 1 2 5 12 7 7 Calculate the 90 confidence interval of the mean and present it in a sentence that shows your understanding of the meaning of the confidence interval b Calculate whether there has been a significant increase over the average 18 reported in the neighborhood newspaper State the hypotheses alpha df and critical value Write a report including all necessary information about your results

3 Costco sells paperback books in their retail stores and wants to examine the relationship between the prices and sales The price of a particular novel was adjusted each week and the weekly sales are in the following table Management would like to use a simple linear regression model that uses prices to predict sales Sales 7 4 5 9 8 8 7 Price 12 11 10 9 8 7 7 The coefficient of determination for this sample is equal to Multiple Choice O 0 273 0 450 0 392

The lengths of a particular animal s pregnancies are approximately normally distributed with mean 276 days and standard deviation o 16 days a What proportion of pregnancies lasts more than 288 days b What proportion of pregnancies lasts between 264 and 284 days c What is the probability that a randomly selected pregnancy lasts no more than 244 days d A very preterm baby is one whose gestation period is less than 252 days Are very preterm babies unusual a The proportion of pregnancies that last more than 288 days is Round to four decimal places as needed b The proportion of pregnancies that last between 264 and 284 days is Round to four decimal places as needed c The probability that a randomly selected pregnancy lasts no more than 244 days is Round to four decimal places as needed d The probability of a very preterm baby is This event than 0 05 Round to four decimal places as needed unusual because the probability is

Steel rods are manufactured with a mean length of 22 centimeter cm Because of variability in the manufacturing process the lengths of the rods are approximately normally distributed with a standard deviation of 0 07 cm Complete parts a to d RECID a What proportion of rods has a length less than 21 9 cm Round to four decimal places as needed

The time required for an automotive center to complete an oil change service on an automobile approximately follows a normal distribution with a mean of 19 minutes and a standard deviation of 3 minutes a The automotive center guarantees customers that the service will take no longer than 20 minutes If it does take longer the customer will receive the service for half price What percent of customers receive the service for half price b If the automotive center does not want to give the discount to more than 5 of its customers how long should it make the guaranteed time limit www a The percent of customers that receive the service for half price is Round to two decimal places as needed

The number of chocolate chips in an 18 ounce bag of Chips Ahoy chocolate chip cookies is approximately normally distributed with a mean of 1262 chips and a standard deviation of 118 chips according to a study by cadets of the U S Air Force Academy a Determine the 28th percentile for the number of chocolate chips in an 18 ounce bag of Chips Ahoy cookies b Determine the number of chocolate chips in a bag of Chips Ahoy that make up the middle 95 of bags c What is the interquartile range of the number of chips in Chips Ahoy cookies FERM a The 28th percentile for the number of chocolate chips in an 18 ounce bag of Chips Ahoy cookies is chocolate chips Round to the nearest whole number as needed

The mean incubation time for a type of fertilized egg kept at a certain temperature is 17 days Suppose that the incubation times are approximately normally distributed with a standard deviation of 2 days Complete parts a through e below a Draw a normal model that describes egg incubation times of these fertilized eggs Choose the correct graph below Click here to view graph b Click here to view graph a Click here to view graph c Click here to view graph d b Find and interpret the probability that a randomly selected fertilized egg hatches in less than 15 days The probability that a randomly selected fertilized egg hatches in less than 15 days is Round to four decimal places as needed

K Frequency Click here to view the sample data Click here to view the table of critical values for normal probability plots a Draw a relative frequency histogram with lower class limit of the first class equal to 0 and class width 20 O A OB Frequency O C A data set represents the wait time in minutes for a random sample of 100 visitors to Disney s Dinosaur Ride in Animal Kingdom Technology was used to obtain a random sample of 40 observations from the original sample of 100 visitors Complete parts a through c below ONW 25 Wait Time in minutes at Dinosaur Ride 20 20 40 Wait Time Wait Time in minutes at Dinosaur Ride 40 Wait Time 60 60 80 80 Q Q Q G Frequency Frequency 30 25 3221 O D Wait Time in minutes at Dinosaur Ride 30 25 0 20 Wait Time in minutes at Dinosaur Ride 20 40 Wait Time 40 Wait Time b Comment on the shape of the distribution Choose the correct answer below A The distribution is bell shaped OB The distribution is skewed right QC The distribution is ckownd loft 60 8 9 60 80 80 G Q Q

Find the z scores that separate the middle 71 of the distribution from the area in the tails of the standard normal distribution The z scores are Use a comma to separate answers as needed Round to two decimal places as needed

Determine the total area under the standard normal curve in parts a through c below a Find the area under the normal curve to the left of z 1 plus the area under the normal curve to the right of z 1 The combined area is 0 3174 Round to four decimal places as needed b Find the area under the normal curve to the left of z 1 52 plus the area under the normal curve to the right o z 2 52 The combined area is Round to four decimal places as needed

The P value measures the strength of evidence O A sometimes against the null hypothesis and sometimes against the alternative hypothesi B the interpretation depends on whether we reject the null hypothesis O C against the alternative hypothesis D against the null hypothesis

A researcher wishes to determine if the use of an herbal extract improves memory Subjects will take the herbal extract regularly during a 10 week period of time After this course of treatment each subject has his or her memory tested using a standard memory test Suppose the scores on this test of memory for all potential subjects taking the herbal extract follow a Normal distribution with mean and standard deviation o 6 Suppose also that in the general population of all people scores on the memory test follow a Normal distribution with mean 50 and standard deviation o 4 The researcher therefore decides to test the hypotheses Ho 50 Ha 50 To do so the researcher has 100 subjects follow the protocol described above The mean score for these students is 55 2 and the P value is less than 0 0001 Suppose that another researcher attempts to replicate the study described above She uses a sample of 10 subjects and observes a sample mean memory score of 55 2 the same as the sample mean described in the first study Which statement is an appropriate to conclusion O A She has obtained the same sample mean as the first researcher so her P value will be the same as that of the first researcher O B She has obtained the same sample mean as the first researcher but her P value will be smaller than that of the first researcher O C She has obtained the same sample mean as the first researcher but her P value will be greater than that of the first researcher OD None of the above

A 99 confidence interval for the mean of a population is computed from a random sample and found to be 6 3 We may conclude that O A there is a 99 probability that u is between 3 and 9 B there is a 99 probability that the true mean is 6 and there is a 99 chance that the true margin of error is 3 O C if we took many many additional random samples and from each computed a 99 confidence interval for approximately 99 of these intervals would contain O D All of the above

testing hypotheses if the consequences of failing to reject a null hypothesis that is actually false are very erious we should O A use a very small level of significance O B insist that the P value be smaller than the level of significance C insist that the level of significance be smaller than the P value D use a very large level of significance

A medical researcher treats 400 subjects who have high cholesterol with a new drug The average decrease in cholesterol level is 90 mg dL after two months of taking the drug Assume that the decrease in cholesterol after two months of taking the drug follows a Normal distribution with unknown mean and standard deviation o 30 Which approach would produce a confidence interval with a smaller margin of error than the 95 confidence interval you computed above O A Give the drug to only 100 subjects rather than 400 because 100 people are easier to manage and control B Give the drug to 500 subjects rather than 400 O C Compute a 99 confidence interval rather than a 95 confidence interval The increase in confidence indicates that we have a better interval OD None of the above

I collect a random sample of size n from a population and from the data collected compute a 95 confidence interval for the mean of the population Which approach would produce a new confidence interval with smaller width smaller margin of error based on these same data O A Use the same confidence level but compute the interval n times Approximately 5 of these intervals will be larger OB Nothing can guarantee that you will get a smaller interval One can only say the chance of obtaining a smaller interval is 0 05 OC Use a smaller confidence level D Use a larger confidence level

A veterinarian collects data on the number of times race horses are raced during their career The researcher finds the average number of races a horse enters is 15 3 with a standard deviation of s 6 8 in a sample of n 20 horses The standard error of the sample mean is given by rounded to three digits O A 1 560 OB 0 358 O C 0 340 O D 1 521

Before conducting a test of significance what should you do O A Set an appropriate significance level O B Determine what sample size you need for your inference to be successful OC Inspect the data you have collected for outliers or other issues that might challenge the assumptions of the partic statistical test you wish to use OD All of the above

The margin of error in a confidence interval refers to O A sampling error B sonresponse error O C measurement error OD All of the above

A group of veterinary researchers plan a study to estimate the average number of enteroliths in horses suffering from them Previously research has shown the variability in the number to be o 2 The researchers wish the margin of error to be no larger than 0 5 for a 99 confidence interval To obtain such a margin of error the researchers need at least OA 106 observations OB 107 observations O C 54 observations OD 53 observations

A statistician wishing to test a hypothesis that students score at least 75 on the final exam in an introductory statistics course decides to randomly select 20 students in the class and have them take the exam early The average score of the 20 students on the exam was 78 and the standard deviation in the population is known to be o 15 The P value for the hypothesis Ho 75 vs Ha H 75 is OA 0 814 OB 0 186 OC 0 371 O D The answer cannot be determined with information provided

Which is an acceptable statement of a null and alternative hypothesis about a mean O A Ho vs Ha O B Ho H vs Ha x OC Ho vs Ha x OD None of the above

A statistician wishing to test a hypothesis that students score at least 75 on the final exam in an introductor statistics course decides to randomly select 20 students in the class and have them take the exam early The average score of the students on the exam was 78 The hypothesis the statistician wants to test is OA HO H 1 75 vs Ha 78 O B Ho H 75 vs Ha 78 OC Ho H 75 75 vs Ha H 75 O D Ho H 75 vs Ha 75

Suppose the population standard deviation is a 5 an SRS of n 100 is obtained and the confidence leve chosen to be 98 The margin of error for estimating a mean u is given by OA 1 2280 B 0 1165 C 1 1650 OD 0 1228

The upper 0 05 critical value of the standard Normal distribution is OA 2 326 OB 1 645 O C 1 960 O D 2 576

A level 0 95 confidence interval is O A any interval with margin of error 0 95 O B a range of values with margin of error 0 95 which is also correct 95 of the time O C a range of values computed from sample data that will contain the true value of the parameter of interest 95 of t time O D a range of values computed from sample data by a method that guarantees that the probability the interval computed contains the parameter of interest is 0 95

As reported by a recent survey the fast food restaurant with the best drive through time had a mean time spent in the drive through of 63 8 seconds Assuming drive through times are normally distributed with 2 9 seconds complete parts a through d below a What is the probability that a randomly selected car will get through the drive through in less than 60 1 seconds The probability is Round to four decimal places as needed b What is the probability that a randomly selected car will spend more than 70seconds in the drive through The probability is Round to four decimal places as needed c What proportion of cars spend between 60 1 and 70seconds in the drive through Round to four decimal places as needed

To calculate a 99 confidence interval the value z in the margin of error should equal O A 2 33 OB 1 645 O C 1 96 OD 2 576

A normal score is the expected z score of a data value assuming the distribution of the random variable is normal Is this statement true or false Choose the correct answer below OA The statement is true OB The statement is false A normal score is the z score of a data value before it is standardized OC The statement is false The normal score is another name for the z score of a data value OD The statement is false The normal score is the area under the normal curve to the left of a coo

Find the value of Za 20 01

Determine the total area under the standard normal curve in parts a through c below a Find the area under the normal curve to the left of z 1 plus the area under the normal curve to the right of z The combined area is Round to four decimal places as needed

A statistic is said to be unbiased if O A the person computing it doesn t favor any particular outcome B it is used for only honest purposes C the mean of its sampling distribution is equal to the true value of the parameter being estimated O D the person who calculated the statistic and the subjects whose responses make up the statistic were

The distribution of actual weights of 8 ounce wedges of cheddar cheese produced at a dairy is Normal with mean 8 1 ounces and standard deviation 0 2 ounces A sample of 10 of these cheese wedges is selected The distribution of the sample mean of the weights of cheese wedges is O A approximately Normal mean 8 1 standard deviation 0 020 B approximately Normal mean 8 1 standard deviation 0 2 O C approximately Normal mean 8 1 standard deviation 0 063 O D It is not possible to tell because the sample size is too small

n a large population of college educated adults the mean IQ is 112 with standard deviation 25 Suppose 300 adults from this population are randomly selected for a market research campaign The probability that the sample mean IQ is greater than 115 is O A 0 981 B 0 019 OC 0 528 OD 0 452

n a large population of college educated adults the mean IQ is 112 with standard deviation 25 Suppose 300 adults from this population are randomly selected for a market research campaign The distribution of the ample mean IQ is O A approximately Normal mean equal to the observed value of the sample mean standard deviation 25 O B approximately Normal mean 112 standard deviation 0 083 O C approximately Normal mean 112 standard deviation 25 O D approximately Normal mean 112 standard deviation 1 443

The incomes in a certain large population of college teachers have a Normal distribution with mean 75 000 and standard deviation 10 000 Sixteen teachers are selected at random from this population to serve on a committee What is the probability that their average salary is more than 77 500 OA 0 1587 OB 0 0228 OC 0 8413 O D essentially 0

If X is a binomial distribution with n 20 and p 1 4 the standard deviation of X is O A 14 063 B 5 O C 3 75 O D 1 936

Suppose X is a random variable with the binomial distribution with n 4 and p 1 4 The probability X is greater than or equal to 1 is A 0 6836 B 0 3164 C 0 0039 O D 0 9961

The amount of milk sold each day by a grocery store varies according to the Normal distribution with mean 13 gallons and standard deviation 12 gallons On a randomly selected day the probability that the store sells at least 154 gallons is OA 0 1587 OB 0 9772 OC 0 8413 OD 0 0228

A local veterinary clinic typically sees 15 of its horses presenting with West Nile virus Last month 100 horses were admitted and it was found that 20 of them had been infected with West Nile virus The probability of seeing 20 or more horses with West Nile virus was calculated based on a Normal distribution with 15 and standard deviation o 12 75 Which statement is TRUE O A Using the Normal approximation to the binomial distribution is justified because X 20 10 O B Using the Normal approximation to the binomial is justified because n is large and exact calculations are too tedious O C Using the Normal approximation to the binomial is justified because np 15 and n 1 p 85 O D All of the above

Event A occurs with probability 0 3 and event B occurs with probability 0 4 If A and B are independent we may conclude that O A P A and B 0 12 O B P A B 0 3 O C P BIA 0 4 O D All of the answer choices are correct

When a fair six sided die is rolled three times this is an example of O A three events that are independent B three outcomes that are disjoint C three events that are independent with three outcomes that are disjoint D None of the answer choices is correct

A college basketball player makes 5 6 of his free throws Assuming free throws are independent the probability that he makes exactly three of his next four free throws is O A 0 0 00 O B O C O D 00 O Q

An event A will occur with probability 0 5 An event B will occur with probability 0 6 The probability that both A and B will occur is 0 1 We may conclude that O A events A and B are independent O B events A and B are disjoint OC either A or B always occurs OD None of the answer choices is correct