Question

When engineers design products, 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 50 adult males. What is the probability that the average weight of these 50 adult males is over 189 pounds?

Give your answer to 4 decimal places. For help on how to input a numeric answer, please see "Instructions for inputting a numeric response."

___________

Answer 1

We have to find the probability that the average weight of the 50 adult males is over 189 pounds. So,we have to find the mean and standard deviation for sample mean and then we could find the probability.

Now, the given mean weight, =197

Standard deviation of the distribution of sample means is

= /√n = 32/√50 =4.53

Now, we have to compute the z-score and then find the probability based on standard normal table.

So,for =189, we have

z= (-)/ = (189-197)/4.53 = -8/4.53= -1.77

So, from the standard normal distribution table,we have the associated probability is 0.0384. Since,we have to find the area to the right, so subtracting from 1 we get,

P(z> -1.77)= 1- (z < -1.77)= 1- 0.0384= 0.9616

Thus, the probability that the average weight of these 50 adult males is over 189 pounds is 0.9616.