Question 1. The capacity of an elevator is 12 people or 1884 pounds. The capacity will be exceeded if 12 people have weights with a mean greater than 1884 divided by 12 equals 157 pounds.1884/12=157 pounds.Suppose the people have weights that are normally distributed with a mean of 167 lb and a standard deviation of 26 lb.
a) Find the probability that if a person is randomly selected, his weight will be greater than 157 pounds. The probability is approximately ______ (Round to four decimal places as needed.)
b) b. Find the probability that 1212 randomly selected people will have a mean that is greater than 157 pounds. The probability is approximately ______ (Round to four decimal places as needed.)
c) Does the elevator appear to have the correct weight limit? Why or why not?
Question 2. Find the critical value zα/2 that corresponds to the given confidence level.
zα/2 = _____ (Round to four decimal places as needed.)
Question 3. An IQ test is designed so that the mean is 100 and the standard deviation is 10 for the population of normal adults. Find the sample size necessary to estimate the mean IQ score of statistics students such that it can be said with 99% confidence that the sample mean is within 3 IQ points of the true mean. Assume that sigmaσequals=10 and determine the required sample size using technology. Then determine if this is a reasonable sample size for a real world calculation.
The required sample size is ____(Round to the nearest integer.)
Question 4. An IQ test is designed so that the mean is 100 and the standard deviation is 19 for the population of normal adults. Find the sample size necessary to estimate the mean IQ score of statistics students such that it can be said with 90% confidence that the sample mean is within 5 IQ points of the true mean. Assume that sigmaσequals=19 and determine the required sample size using technology. Then determine if this is a reasonable sample size for a real world calculation.
The required sample size is ____(Round to the nearest integer.)