n USE SALT (a) If the distribution is normal, what is the probability that the sample mean hardness for a random sample of 8 pins is at least 51? (b) What is the (approximate) probability that the sample mean hardness for a random sample of 38 pins is at least 51?
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- Imagine a distribution of sample means for samples of n = 25 selected from a population with a mean of μ = 25 and a standard deviation of σ = 5. In the box below, report three things for this distribution of sample means: its shape, its expected value, and its standard error. (Any of your three answers that are rounded numbers should be rounded t4. The time required for all cross-country skiers to complete a race has a normal distribution with a mean of 46 minutes and a standard deviation of 6 minutes. You choose a random sample of six skiers, and the mean of the sample is denoted i. What are the mean and standard deviation of ?A personality test has a subsection designed to assess the "honesty" of the test-taker. Suppose that you're interested in the mean score, µ, on this subsection among the general population. You decide that you'll use the mean of a random sample of scores on this subsection to estimate u. What is the minimum sample size needed in order for you to be 90% confident that your estimate is within 3 of u? Use the value 23 for the population standard deviation of scores on this subsection. Carry your intermediate computations to at least three decimal places. Write your answer as a whole number (and make sure that it is the minimum whole number that satisfies the requirements). (If necessary, consult a list of formulas.)
- 11. The amount of time that a drive-through bank teller spends on a customer is a random variable with a mean μ = 6.4 minutes and a standard deviation o=3.5 minutes. If a random sample of 49 customers is observed, find the probability that their mean time at the teller's window is (a) at most 5.6 minutes; (b) more than 7.4 minutes; (c) at least 6.4 minutes but less than 7.0 minutes. Click here to view page 1 of the standard normal distribution table.¹ Click here to view page 2 of the standard normal distribution table.² (a) The probability that the mean time is at most 5.6 minutes is (Round to four decimal places as needed.) (b) The probability that the mean time is more than 7.4 minutes is (Round to four decimal places as needed.) (c) The probability that the mean time is between 6.4 minutes and 7.0 minutes is (Round to four decimal places as needed.)A personality test has a subsection designed to assess the "honesty" of the test-taker. Suppose that you're interested in the mean score, μ, on this subsection among the general population. You decide that you'll use the mean of a random sample of scores on this subsection to estimate μ. What is the minimum sample size needed in order for you to be 90% confident that your estimate is within 3 of μ? Use the value 23 for the population standard deviation of scores on this subsection. Carry your intermediate computations to at least three decimal places. Write your answer as a whole number (and make sure that it is the minimum whole number that satisfies the requirements).Suppose that the mean value of interpupillary distance (the distance between the pupils of the left and right eyes) for adult males is 65 mm and that the population standard deviation is 5 mm. (a) If the distribution of interpupillary distance is normal and a random sample of n = 25 adult males is to be selected, what is the probability that the sample mean distance x for these 25 will be between 63 and 67 mm?(Round all your intermediate calculations to four decimal places. Round the answers to four decimal places.) P = (b) Suppose that a sample of 100 adult males is to be obtained. Without assuming that interpupillary distance is normally distributed, what is the approximate probability that the sample mean distance will be between 63 and 67 mm? (Round all your intermediate calculations to four decimal places. Round the answers to four decimal places.) P = Without assuming that interpupillary distance is normally distributed, what is the approximate probability that the sample mean…
- 3a) The mean IQ of 200 patients in a psychiatric hospital is 91, with a variance of 16, and the distribution is highly negatively skewed. Between what two IQ scores would we expect to find at least 160 of the patients falling? b) If the distribution was mound-shaped and symmetrical, with the same mean and standard deviation as in part A, approximately how many patients would have IQ scores at or below the 5th percentile or above a score of 97? Answers: a) 82 to 100 b) 28.5 or 292. Suppose X is a normally distributed random variable with a mean of 9.00. If the probability that X is less than 9.66 is 0.67, then what is the standard deviation of X?38)
- Given a population mean of 3.4, and a population standard deviation of 1.2, how would I use the central limit theorem to find the probability the mean size given a random size sample of n = 100, would be more than 3?A personality test has a subsection designed to assess the "honesty" of the test-taker. Suppose that you're interested in the mean score, μ, on this subsection among the general population. You decide that you'll use the mean of a random sample of scores on this subsection to estimate H. What is the minimum sample size needed in order for you to be 99% confident that your estimate is within 5 of u? Use the value 23 for the population standard deviation of scores on this subsection. Carry your intermediate computations to at least three decimal places. Write your answer as a whole number (and make sure that it is the minimum whole number that satisfies the requirements). (If necessary, consult a list of formulas.) Continue 2 3 X S $ 4 O % 5 6 & 7 Ⓒ2022 McGraw Hill LLC. All Rights Reserved. Terms of Use Privacy Center 8 9 ) Submit Assignment Accessibility 0 ? OO1. Service time for a customer coming through a checkout counter in a retail store is a random variable with the mean of 10.0 minutes and standard deviation of 4.0 minutes. Suppose that the distribution of service time is fairly close to a normal distribution. Suppose there are two counters in a store, n₁ = 41, customers in the first line and m₂ = 51 customers in the second line. Find the probability that the difference between the mean service time for the shorter line and the mean service time for the longer X₂ one ¹2 is more than 0.4 minutes. Assume that the service times for each customer can be regarded as independent random variables.