Statistics Questions

d the mode s for the following group of data items 37 34 33 32 38 35 31 33 ect the correct choice below and if necessary fill in the answer box within you A The mode s is are B There is no mode Use a comma to separate answers as needed

K Use six intervals starting with 0 24 Perform the following a Group the data as indicated b Prepare a frequency distribution with a column for intervals and frequencies c Construct a histogram d Construct a frequency polygon a Tally the given data falling into each interval Choose the correct table below OA OB Interval 0 24 24 48 48 72 H 72 96 96 120 120 149 Tally Will 441 Interval 0 24 25 49 50 74 411 75 99 Hi 100 124 III 125 149 Tally O C Interval 0 24 24 48 48 72 72 96 96 120 120 149 1 Tally 441 1 17 118 115 71 129 25 28 44 127 82 57 136 45 73 63 143 77 72 122 11 46 35 83 82 2 97 84 96 91 36 85 147 32 82 12 101 O D Interval Tally 0 24 Willl LH1 25 49 50 74 75 99 LH1 LH1 IIII 100 124 1 125 149 IIII

Emerald Bazaar has a materials price standard of 2 00 per pound Six thousand pounds of materials were purchased at 2 20 a pound The actual quantity of materials used was 6 000 pounds although the standard quantity allowed for the output was 5 400 pounds Emerald Bazaar s materials price variance is

he acreage in thousands of acres of the 39 U S National Parks is shown here Construct a frequency distribution for the data sing eight classes 41 36 183 520 650 505 196 760 66 338 61 77 462 94 70 143 233 775 233 236 13 308 27 217 106 52 75 265 132 28 46 539 169 64 77 5 52 402 220

nd the range and standard deviation for the set of numbers 110 123 141 143 147 196 ne range is

Suppose 16 coins are tossed Find the probability of getting the following result using the binomial probability formula and the normal curve approxim Exactly 4 heads Use the table of areas under the standard normal curve given below Click here to view page 1 Click here to view page 2 Click here to view page 3 Click here to view page 4 Click here to view page 5 Click here to view page 6 Binomial probability Round to 4 decimal places

A certain type of light bulb has an average life of 1900 hours with a standard deviation of 50 hours The length of life of the bulb can be closely approximated by a normal curve An amusem buys and installs 30 000 such bulbs Find the total number that can be expected to last less than 1960 hours Click here to view page 1 of the Areas under the Normal Curve Table Click here to view page 2 of the Areas under the Normal Curve Table The number of light bulbs that can be expected to last less than 1960 hours is BEEB

Find the percent of the total area under the standard normal curve between the following z scores This problem can be solved using technology or the table for the standard normal cur text Click here to view page 1 of the table Click here to view page 2 of the table z 1 1 and z 0 8 The percent of the total area between z 1 1 and z 0 8 is Round to the nearest whole percent as needed C

7 10 15 17 26 The mean is Round to the nearest tenth as needed

for normal distributions where 0 oro 1 hoose the correct answer below OA Az score is found with the formula z A OB Az score is found with the formula z OC Az score is found with the formula z A X H OD A z score is found with the formula z x b PIO X H X

peak in a normal curve appears directly above in the blank below peak in a normal curve appears directly above the standard deviation the z score x equals 1

Find a z score satisfying the following condition 0 of the total area is to the right of z Click here to view page 1 of the Areas under the Normal Curve Table Click here to view page 2 of the Areas under the Normal Curve Table Round to the nearest hundredth as needed

Find the range and standard deviation of the set of numbers 34 28 38 36 34 29 32 The range is

certain distribution of numbers the mean is 70 with a standard deviation of 4 Chebyshev s rem states that for any set of numbers the fraction that will lie within k standard deviations of 1 mnean for k 1 is at least 1 Use Chebyshev s theorem to tell the probability that a k ber lies between 58 and 82 The probability a number lies between 58 ar Round to the nearest thousandth as needec

Chebyshev s Theorem states that for any set of numbers the fraction that will lie within k standard 1 deviations of the mean is at least 1 Use this theorem to find the fraction of all the numbers of a data set that must lie within 3 standard deviations from the mean At least of all numbers must lie within 3 standard deviations from the mean Type an integer or a fraction

nd the median for the following list of numbers 103 118 131 139 148 164 he median is Type an integer or a decimal

a Let X be an exponential random variable with a parameter 0 Show that XX is an exponential random variable of parameter 1

4 Suppose that the number of cars visiting New Paltz has Poisson distribution with a parameter A 0 There are three types of cars diesel sedan and truck The probability of randomly chosen car is a diesel sedan or truck is P P2 and p3 with p P2 P3 1 and the event of each car being a certain type is independent of each other Let X Y Z be numbers of diesel cars sedans or trucks during one day a Suppose that there are n distinct items We want to divide n items into three groups group A B and C with a b and c elements with a b c n Show that the number of different grouping is c n a b c alxblxc b Show that a b c a b c P1P2P3 X a b c a b c 1

Consider two normal distributions one with mean 11 and standard deviation 3 the other with mean 14 and standard deviation 3 Answer the following statements using true or false a The two distributions have the same shape answer b The two distributions are centered at the same place answer Note You can earn partial

5 1 point Let p z be the density function given by Find the mean value of p z p z 0 if 0 z 13 if 13 23 otherwise

The shelf life of a battery produced by one major company is known to be Normally distributed with a mean life of 3 years and a standard deviation of 0 9 years What value of shelf life do 16 of the battery shelf lives fall below Round your answer to one decimal place Answer year

Laticia randomly selected 25 of the seventh grade students in her school and asked them their favorite season Of the students surveyed 51 chose summer as their favorite season Based on the data what is the most reasonable prediction of the number of students in her school who would choose summer as their favorite seventh grade season A B C D 15 75 150 200

Complete parts a c y X y y 1 2 2 1 3 0 a Find a cubic function that models the data in the table Report the model with three decimal pla Linear 4 4 Cubic 5 8 b Find a linear function that models the data Report the model with three decimal places 6 16 c Visually determine which model is the better fit for the data

D Cost Model Find a linear regression model for the weekly cost data using as the independent variable C x mx k Round m to 1 decimal place and round to the nearest integer Use this cost model to answer questions 9 15 below Question 9 Use the cost model above to answer this question What is m Round to 1 decimal place 2 pts

1 point Scores on a certain intelligence test for children between ages 13 and 15 years are approximately normally distributed with 106 and o 24 a What proportion of children aged 13 to 15 years old have scores on this test above 92 NOTE Please enter your answer in decimal form For example 45 23 should be entered as 0 4523 Answer 0 6445 b Enter the score which marks the lowest 20 percent of the distribution Answer 78 3 c Enter the score which marks the highest 15 percent of the distribution Answer 135 6

Revenue Model Use the price model above to construct a revenue model Find a model for the weekly revenue using a as the independent variable NOTE Do not calculate another regression Use the price equation to find a model for revenue R x p z R z p z a bx cz z az bz cz Use this revenue model to answer questions 3 8 below Question 3 Use the revenue model above to answer this question What is a Round to the nearest integer 3 pts

Using diaries for many weeks a study on the lifestyles of visually impaired students was conducted The students kept track of many lifestyle variables including how many hours of sl obtained on a typical day Researchers found that visually impaired students averaged 8 88 hours of sleep with a standard deviation of 2 55 hours Assume that the number of hours c sleep for these visually impaired students is normally distributed a What is the probability that a visually impaired student gets less than 6 4 hours of sleep 4 answer b What is the probability that a visually impaired student gets between 6 9 and 8 6 hours of sleep answer c Twenty percent of students get less than how many hours of sleep on a typical day answer hours

0 Yaster Outfitters manufactures and sells extreme cold sleeping bags The table below shows the price demand and total cost data where M p is the wholesale price in dollars of a sleeping bag for a weekly demand of a sleeping bags C is the total cost in dollars of producing a sleeping bags sleeping bags p 240 235 155 50 95 120 180 220 C 13 000 14 300 18 500 21 000 Use this data to create regression models to answer all of the questions below Price Model Find a quadratic regression equation for the price demand data using as the independent variable pa ba c Round a to the nearest integer round b to 2 decimal places and round c to 4 decimal places Use this price model to answer question 1 2 below

In a random sample 15 people working for a startup technology company were asked about the number of hours they spent exercising during the previous month Their answers were as follows in hours 36 22 28 29 40 33 37 39 40 34 21 39 40 38 and 36 Find the mean and the range for the sample Estimate your answers to 1 decimal place Find the standard deviation and the median for the sample Estimate any irrational answers to two decimal places

Consider two normal distributions one with mean 10 and standard deviation 3 the other with mean 14 and standard deviation 2 Answer the following statements using true or false a The two distributions have the same shape answer b The two distributions are centered at the same place answer

Show that T PP defined by T p x p x p x is an isomorphism Since the dimensions of the domain and codomain are the same it suffices to show that T is one to one Let p x a a x ax Then p x p x a a a 2a x x 1 x But then the coefficient of x 1 is 0 an 1 so that an 1 If p x p x 0 then the coefficient of x is Select so that a a for all i Thus p x so that T is one to one and is thus an isomorphism We continue this process determinim

Each hour for several hours the owner of a bakery recorded the number of customers who entered the store The box and whisker plot sometimes called a boxplot summarizes the data 10 15 20 25 30 Number of customers 35 40 45 D 50 Use the box and whisker plot to answer the following a What is the median number of customers 0 b What is the smallest number of customers 0 c What is the first quartile Q of the numbers of customers X

ubian goats of 35 Nubian goats and record the birth weights Assume it is known that the population standard deviation of the birth weights of Nubian goats is 1 36 kg Based on your sample follow the steps below to construct a 90 confidence interval for the population mean of the birth weights for all Nubian goats If necessary consult a list of formulas a Click on Take Sample to see the results from your random sample of 35 Nubian goats Take Sample Sample size 0 Point estimate 0 Population standard deviation Critical value 0 Compute 0 00 Number of goats Sample mean 0 00 Enter the values of the sample size the point estimate for the population mean the population standard deviation and the critical value you need for your 90 confidence interval Choose the correct critical value from the table of critical values provided When you are done select Compute 35 2 00 4 31 Standard error Margin of error 4 00 Sample standard 90 confidence interval 90 confidence interval deviation 1 13 6 00 X b Based on your sample enter the lower and upper limits to graph the 90 confidence interval for the population mean of the birth weights for all Nubian goats Confidence level 99 95 90 Population standard deviation 1 36 8 00 Critical value 20 005 2 576 1 960 20 025 20 050 1 645 10 00 10 00

Your employer offers a 401 k plan with a 27 match and you set a goal of retiring in 31 years with an amount of money which has the same buying power that 1 6 million dollars has today If the account earns an annual interest rate of 1 and the expected annual rate of inflation is 1 1 how much should YOU contribute each month to the 401 k Round your answer to the nearest dollar

Refer to the data table below Complete parts a through d Click on the icon to view the data table a Find the best regression equation with IQ score as the response variable Use predictor variables of brain volume VOL and or weight W Select the correct choice and fill in the answer be complete your choice Round to four decimal places as needed OA A IQ VOL W OB IQ O C 1Q W VOL IQ Brain Volume and Weight Data Table IQ 96 90 87 88 101 103 104 97 127 126 102 95 92 87 94 85 96 115 112 Brain Volume cm 1004 962 1036 1026 1281 1271 1051 1077 1036 1068 1173 1078 1067 1103 1345 1437 1028 1098 1205 Body Weight kg 57 914 58 809 64 942 58 803 63 659 61 002 132 957 107 286 62 806 83 574 61 679 61 526 83 699 79 996 97 542 99 727 81 153 88 823 79 914 X

Use the given data set to complete parts a through c below Use 0 05 13 8 8 14 8 75 X y Click here to view a table of critical values for the correlation coefficient a Construct a scatterplot Choose the correct graph below A 10 9 13 AY 10 8 6 4 2 04 0 0 0000 4 8 12 16 B Ay 10 8 6 4 2 0 9 8 77 4 12 16 Q G 11 9 26 14 8 11 C Ay 10 8 6 4 2 0 4 6 6 13 8 12 16 Q 4 3 09 12 9 14 OD Ay 10 8 6 4 2 0 0 4 8 b Find the linear correlation coefficient r then determine whether there is sufficient evidence to support the claim of a linear correlation between the two variables The linear correlation coefficient is r Round to three decimal places as needed 7 7 26 X 12 16 Q Q

A Suppose IQ scores were obtained for 20 randomly selected sets of couples The 20 pairs of measurements yield x 97 76 y 94 9 r 0 832 P value 0 000 and y 6 86 0 9x where x represents the IQ score of the husband Find the best predicted value of y given that the husband has an IQ of 95 Use a significance level of 0 05 Click the icon to view the critical values of the Pearson correlation coefficient r The best predicted value of vis

Heights cm and weights kg are measured for 100 randomly selected adult males and range from heights of 136 to 191 cm and weigh of 40 to 150 kg Let the predictor variable x be the first variable given The 100 paired measurements yield x 167 50 cm y 81 51 kg r 0 342 P value 0 000 and y 105 1 05x Find the best predicted value of y weight given an adult male who is 176 cm tall Use 0 01 significance level Click the icon to view the critical values of the Pearson correlation coefficient r The best predicted value of y for an adult male who is 176 cm tall is Round to two decimal places as needed kg

3 When Hannah wakes up on time there is a 10 chance she will miss the bus for school If she oversleeps there is a 50 chance she will miss the bus On average Hannah oversleeps one morning a week a What is the probability that Hannah will wake up late and miss the bus b What is the probability that Hannah will miss the bus SCHOOL BUS

In a particular survey of internet users 3633 respondents say that they use social networking sites and 1402 respondents say that they do not use social networking sites What is the probability that a randomly selected person uses a social networking site Does that result suggest that it is likely with a probability of 0 5 or greater for someone to use social networking sites The probability that a randomly selected person uses a social networking site is Round to three decimal places as needed

Households are randomly selected and partitioned into groups of four For those groups the random variable x is the number of households with a printer Determine whether a probability distribution is given If a probability distribution is given find its mean and standard deviation If a probability distribution is not given identify the requirements that are not satisfied Does the table show a probability distribution Select all that apply 0 A Yes the table shows a probability distribution B No not every probability is between 0 and 1 inclusive C No the numerical values of the random variable x are not associated with probabilities D No the random variable x is categorical instead of numerical E No the sum of all the probabilities is not equal to 1 0 1 2 3 4 0 145 0 335 0 357 0 138

Groups of adults are randomly selected and arranged in groups of three The random variable x is the number in the group who say that they would feel comfortable in a self driving vehicle Determine whether a probability distribution is given If a probability distribution is given find its mean and standard deviation If a probability distribution is not given identify the requirements that are not satisfied X 0 1 2 3 P x 0 363 0 427 0 183 0 027 Does the table show a probability distribution Select all that apply A Yes the table shows a probability distribution B No not every probability is between 0 and 1 inclusive C No the random variable x s number values are not associated with probabilities D No the sum of all the probabilities is not equal to 1 E No the random variable x is categorical instead of numerical

mal curve Those with z scores above 2 2 will receive an A those between 2 2 and 0 8 will receive a B those between 0 8 and 0 9 will receive a C those between 0 9 and 2 2 will receive a D and those under 2 2 will receive an F Determine the percent of grades that will be A B C D and F Click here to view page 1 of the standard normal distribution table Click here to view page 2 of the standard normal distribution table 1 39 of the grades are A s Round to two decimal places as needed 19 8 of grades are B s Round to two decimal places as needed 60 4 of grades are C s Round to two decimal places as needed 17 02 of grades are D s Round to two decimal places as needed of grades are F s Pound to two decimal places as needed

A computer randomly selects a number from 1 through 50 Two selections are made by the computer to create an ordered pair of numbers How many elements are in the sample space for this experiment Select one Oa 2500 b 100 C 50 Od 2450 e 2000

Mr Sanderson marks his class on a normal curve Those with z scores above 2 2 will receive an A those between 2 2 and 0 8 will receive a B those etween 0 8 and 0 9 will receive a C those between 0 9 and 2 2 will receive a D and those under 2 2 will receive an F Determine the percent o rades that will be A B C D and F Click here to view page 1 of the standard normal distribution table Click here to view page 2 of the standard normal distribution table of the grades are A s Round to two decimal places as needed

Assume the annual day care cost per child is normally distributed with a mean of 8000 and a standard deviation of 1400 What percent of day care costs are more than 8700 annually Click here to view page 1 of the standard normal distribution table Click here to view page 2 of the standard normal distribution table Round to two decimal places as needed

1 The table shows the number of turtles hatched at a zoo each year since 2003 a Find the line of best fit b Predict the number of turtles to be hatched in 2011 c Estimate the Turtles Hatched Year 2003 21 2004 17 2005 16 2006 2007 16 14

A poll showed that 48 out of 120 randomly chosen graduates of California medical schools last year intended to specialize in family practice What is the width of a 90 percent confidence interval for the proportion that plan to specialize in family practice Multiple Choice SHEBREONE O O 0736 1 0447 0894 1 0876

Use the set of data below to do the following a Draw a scatter diagram b Find the value of r c Determine whether a correlation exists at 0 05 d Determine whether a correlation exists at x 0 01 Click the icon to view the correlation coefficient r for various values of n and a X 23 34 32 42 50 y 25 36 27 32 38 The formula for the correlation coefficient is n Exy Ex Ey r n Ex Ex n Ey Ey C a Choose the scatter plot that best represents the given data OA Ay 50 40 30 20 10 0 O C Ay 50 40 30 20 10 PIT 0 O 0 8 16 24 32 40 O O 00 O X O 60 A 0 10 20 30 40 50 X 2 Q OB Ay 40 30 20 10 ott D Ay 0 10 2030 40 50 40 O b O 30 20 10 0 O O d o d O Po X 0 10 20 30 40 50 b The value of ris Round to the nearest thousandth as needed N X

4 51 Pitchers The table shows the number of wins and the num ber of strike outs SO for 40 baseball pitchers in the major leagues in 2011 Source 2011 MLB PITCHING STATS http www baseball reference com leagues MLB 2011 pitching leaders shtml accessed via StatCrunch Owner IrishBlazeFighter a Make a scatterplot of the data and state the sign of the slope from the scatterplot Use strike outs to predict wins b Use linear regression to find the equation of the best fit line Insert the line on the scatterplot using technology or by hand c Interpret the slope d Interpret the intercept and comment on it Wins 21 19 17 24 18 13 13 14 16 11 21 12 13 15 16 13 19 13 16 16 SOS 248 220 238 250 198 139 220 194 225 146 198 179 175 178 206 117 230 161 197 192 Wins 12 13 16 8 10 9 9 11 14 14 11 14 9 15 16 11 12 13 17 13 SOS 158 191 158 134 197 123 96 178 111 126 191 222 185 182 169 166 218 126 207 158