Question

In engineering and product design, it is important to consider the weights of people so that airplanes or elevators aren't overloaded. Based on data from the National Health Survey, we can assume the weight of adult males in the US has a mean weight of 197 pounds and standard deviation of 32 pounds. We randomly select 64 adult males. What is the probability that the average weight of these 64 adult males is over 192 pounds?

Give your answer to 4 decimal places.

** Please tell me the answer as well as a step by step process as to how you got the answer ** Thanks!

Answer 1

Here sample size is n=64>30 so as per central limit theorem distribution of sample mean is normally distributed with mean=197 and standard deviation is

Now we need to find

As sample mean is normally distributed we can convert sample mean to z