Question

A random variable is normally distributed. It has a mean of 245 and a standard deviation of 21. a.) For a sample of size 10, state the mean of the sample mean and the standard deviation of the sample mean. b.) For a sample of size 10, find the probability that the sample mean is more than 230.

Answer 1

A random variable is normally distributed. It has a mean of 245 and a standard deviation of 21. a.) For a sample of size 10, state the mean of the sample mean

Sample mean is 245

For a sample of size 10, state the standard deviation of the sample mean

Standard error of the mean formula is

σ_M = standard error of the mean

σ = the standard deviation of the original distribution

N = the sample size

√N = root of the sample

standard error of the mean = standard deviation of distribution/sqrt(sample size)

=21/SQRT(10)

=6.641

For a sample of size 10, find the probability that the sample mean is more than 230.

μ = 245 and σ = 21

=(230-245)/21/SQRT(10) = -0.2259 = 0.23

value 0.23 , to find the area of Z and subtract from 1

0.4090 is z score of 0.23

=1-0.4090

=0.591