Statistics Questions & Answers

The denoted \( \hat{p} \), is given by the formula \( \hat{p}= \) where x is the number of individuals with a specified characteristic in a sample of n individuals.

Describe the sampling distribution of \( \hat{p} \). Assume the size of the population is 20,000 . \( n=700, p=0.6 \) Choose the phrase that best describes the shape of the sampling distribution of \( \hat{p} \) below. A. Approximately normal because \( n \leq 0.05 \mathrm{~N} \) and \( n p(1-p)<10 \). B. Approximately normal because \( n \leq 0.05 \mathrm{~N} \) and \( n p(1-p) \geq 10 \). C. Not normal because \( n \leq 0.05 \mathrm{~N} \) and \( n p(1-p) \geq 10 \). D. Not normal because \( n \leq 0.05 \mathrm{~N} \) and \( n p(1-p)<10 \).

Multipart Classification Classify each statement as describing a joint, marginal, or conditional relative frequency. a. In a study on age and driving safety, \( 33 \% \) of drivers were considered younger and a high accident risk. b. In a study on age and driving safety, \( 45 \% \) of older drivers were considered a high accident risk. c. In a study on age and driving safety, \( 67 \% \) of drivers were classified as younger. d. In a pre-election poll, \( 67 \% \) of the respondents who preferred the incumbent were men. e. In a pre-election poll, \( 33 \% \) of women preferred the challenger. f. In a pre-election poll, \( 16 \% \) of respondents were men who preferred the challenger.

16 Suppose that the lifetimes of light bulbs are approximately normally distributed, with a mean of 56 hours and a standard deviation of 3.3 hours. With this inf (a) What proportion of light bulbs will last more than 62 hours? (b) What proportion of light bulbs will last 51 hours or less? (c) What proportion of light bulbs will last between 57 and 61 hours? (d) What is the probability that a randomly selected light bulb lasts less than 46 hours? (a) The proportion of light bulbs that last more than 62 hours is (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 17 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 (b) If the automotive center does not want to give the discount to more than \( 2 \% \) of its customers, how long should it make the guaranteed time limit? (a) The percent of customers that receive the service for half-price is (Round to two decimal places as needed.)

16 The mean incubation time of fertilized eggs is 22 days. Suppose the incubation times are approximately normally distributed with a standard deviation of 1 day. (a) Determine the 11 th percentile for incubation times. (b) Determine the incubation times that make up the middle \( 95 \% \) of fertilized eggs. (a) The 11 th percentile for incubation times is \( \square \) days. (Round to the nearest whole number as needed.)

16 Suppose that the lifetimes of light bulbs are approximately normally distributed, with a mean of 56 hours and a standard deviation of 3.3 hours. With this (a) What proportion of light bulbs will last more than 62 hours? (b) What proportion of light bulbs will last 51 hours or less? (c) What proportion of light bulbs will last between 57 and 62 hours? (d) What is the probability that a randomly selected light bulb lasts less than 46 hours? (a) The proportion of light bulbs that last more than 62 hours is 0.0344 . (Round to four decimal places as needed.) (b) The proportion of light bulbs that last 51 hours or less is 0.0651 (Round to four decimal places as needed.)

16 Suppose that the lifetimes of light bulbs are approximately normally distributed, with a mean of 56 hours and a standard deviation of 3.3 hours. 1 (a) What proportion of light bulbs will last more than 62 hours? (b) What proportion of light bulbs will last 51 hours or less? (c) What proportion of light bulbs will last between 57 and 62 hours? (d) What is the probability that a randomly selected light bulb lasts less than 46 hours? (a) The proportion of light bulbs that last more than 62 hours is (Round to four decimal places as needed.)

The number of chocolate chips in an 18 -ounce bag of chocolate chip cookies is approximately normally distributed with a mean of 1252 chips and standard deviation 129 chips. (a) What is the probability that a randomly selected bag contains between 1100 and 1400 chocolate chips, inclusive? (b) What is the probability that a randomly selected bag contains fewer than 1125 chocolate chips? (c) What proportion of bags contains more than 1200 chocolate chips? (d) What is the percentile rank of a bag that contains 1450 chocolate chips? (a) The probability that a randomly selected bag contains between 1100 and 1400 chocolate chips, inclusive, is (Round to four decimal places as needed.)

The number of chocolate chips in an 18 -ounce bag of chocolate chip cookies is approximately normally distributed with a mean of 1252 chips and standard deviation 129 chips. (a) What is the probability that a randomly selected bag contains between 1100 and 1400 chocolate chips, inclusive? (b) What is the probability that a randomly selected bag contains fewer than 1025 chocolate chips? (c) What proportion of bags contains more than 1225 chocolate chips? (d) What is the percentile rank of a bag that contains 1425 chocolate chips? (a) The probability that a randomly selected bag contains between 1100 and 1400 chocolate chips, inclusive, is 0.7560. (Round to four decimal places as needed.) (b) The probability that a randomly selected bag contains fewer than 1025 chocolate chips is 0.0392 . (Round to four decimal places as needed.) (c) The proportion of bags that contains more than 1225 chocolate chips is 0.5827 . (Round to four decimal places as needed.) (d) The percentile rank of a bag that contains 1425 chocolate chips is 92 . (Round to the nearest integer as needed.)