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(Solved): An elevator has a placard stating that the maximum capacity is 1376lb8 passengers, So, 8 adult m ...
An elevator has a placard stating that the maximum capacity is passengers, So, 8 adult male passengers can have a mean weight of up to pounds. If the elevator is loaded with 8 adult male passengers, find the probability that it is overloaded because they have a mean weight greater than (Assume that weights of males are normally distributed with a mean of and a standard deviation of ) Does this elevator appear to be safe? The probability the elevator is overloaded is (Round to four decimal places as needed) Does this elevator appear to be safe? A. No, 8 randomly selected people will never be under the weight limit B. No, there is a good chance that 8 randomly selected adult male passengers will exceed the elevator capacity C. Yes, there is a good chance that 8 randomly selected people will not exceed the elevator capacity D. Yes, 8 randomly selected aduit male passengers will always be under the weight limit
Expert Answer
To find the probability that the elevator is overloaded due to the mean weight of 8 adult male passengers being greater than 172 lb, we can use the concept of the sampling distribution of the sample mean. Given: Mean weight of adult males (?) = 179 lb Standard deviation of adult males (?) = 31 lb Sample size (n) = 8 The mean weight of a sample of 8 adult male passengers can be considered as the sample mean (x?), which follows a normal distribution. The mean of the sample mean is equal to the population mean (?) and the standard deviation of the sample mean (?x?) is calculated by dividing the population standard deviation (?) by the square root of the sample size (n).