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 177 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 190 pounds?

0.002

Step-by-step explanation:

We need to estimate the standard error of the mean, so we can use it as a standard deviation of the sample of 50 males.

Standard error of the mean = standard deviation/√n

Standard error of the mean = 32/√50 = 4.52

Now we can use this Standard error of the mean to estimate z as follows:

Z = (x - mean) / standard deviation

Z = (190-177) / 4.52

Z = 2.87

Using a Z table we can find probability that mean is under 190

P (z<190) = 0.998

For the probability that the mean exceed 190 lbs we substract from 1

P (z>190) = 1 - 0.998 = 0.002