An elevator has a placard stating that the maximum capacity is 3700 Ib-26 passengers. So, 26 adult male passengers can have a mean weight of up to 3700 / 26 = 142 pounds. Assume that weights of males are normally distributed with a mean of 187 lb and a standard deviation of 38 Ib. a. Find the probability that 1 randomly selected adult male has a weight greater than 142 Ib. b. Find the probability that a sample of 26 randomly selected adult males has a mean weight greater than 142 Ib c. What do you conclude about the safety of this elevator? a. The probability that 1 randomly selected adult male has a weight greater than 142 lb is . (Round to four decimal places as needed.) b. The probability that a sample of 26 randomly selected adult males has a mean weight greater than 142 lb is . (Round to four decimal places as needed.) c. Does this elevator appear to be safe? O A. No, because 26 randomly selected people will never be under the weight limit. O B. Yes, because there is a good chance that 26 randomly selected people will not exceed the elevator capacity. O C. No, because there is a good chance that 26 randomly selected adult male passengers will exceed the elevator capacity. O D. Yes, because 26 randomly selected adult male passengers will always be under the weight limit.

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.4: Distributions Of Data

Problem 19PFA

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An elevator has a placard stating that the maximum capacity is 3700 Ib-26 passengers. So, 26 adult male passengers can have a mean weight of up to 3700 / 26 = 142 pounds. Assume that weights of males are normally distributed with a mean of 187 lb and a standard deviation of 38 Ib. a. Find the probability that 1 randomly selected adult male has a weight greater than 142 Ib. b. Find the probability that a sample of 26 randomly selected adult males has a mean weight greater than 142 Ib c. What do you conclude about the safety of this elevator? a. The probability that 1 randomly selected adult male has a weight greater than 142 lb is __. (Round to four decimal places as needed.) b. The probability that a sample of 26 randomly selected adult males has a mean weight greater than 142 lb is __. (Round to four decimal places as needed.) c. Does this elevator appear to be safe? O A. No, because 26 randomly selected people will never be under the weight limit. O B. Yes, because there is a good chance that 26 randomly selected people will not exceed the elevator capacity. O C. No, because there is a good chance that 26 randomly selected adult male passengers will exceed the elevator capacity. O D. Yes, because 26 randomly selected adult male passengers will always be under the weight limit.

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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