Youre told that XN836 Suppose you find the mean of 25 observ

You\'re told that X=N(8,36). Suppose you find the mean of 25 observations.

a. What is the distribution of the mean?

b. What is the probability of obtaining a mean=7.5 or less if X=N(8,36)?

Solution

You\'re told that X=N(8,36). Suppose you find the mean of 25 observations.

Variance of X=36

Sd of X =sqrt(36) =6

Standard deviation of mean of X is sd/sqrt(n) =6/sqrt( 25) =6/5 =1.2

distribution of the mean is N( mean, variance) = N(8,1.44)

or mean of X is with mean 8 and with standard deviation 1.2

b. What is the probability of obtaining a mean=7.5 or less if X=N(8,36)?

Z value for 7.5, z=( 7.5 - 8)/1.2 =-0.42

P( x 7.5) = P( z < -0.42) = 0.3372