Determining the probability using mean and standard deviation.

The weights of adult Americans are normal with a meanof 164 lbs. and a standard deviationof 24 lbs. Two random samples are taken with 10 adult Americans in each sample.

(a) What is the probabilitythat both samples have a mean greater than 180 lbs.?

(b) What is the probability that, when the two samples are put together, the mean weight of all 20 people will be greater than 180 lbs?

(c) Compare the results in (a) and (b). Explain.

a) X – weight – Normal (mean=164, sd=24)

n1=10 n2=10 n-sample size

Xbar1 – Normal (mean=164, sd=24/sqrt10=7.5)

P(Xbar1>180) = P(z> …

The solution determines the probability of weight using mean and standard deviation.