Explore BrainMass

# Determining the probability using mean and standard deviation.

This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

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

(a) What is the probability that 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.

© BrainMass Inc. brainmass.com March 4, 2021, 5:37 pm ad1c9bdddf
https://brainmass.com/statistics/dispersion-and-spread-of-data/determining-probability-mean-standard-deviation-2709

#### Solution Preview

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> ...

#### Solution Summary

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

\$2.49