Mathematics
The Sampling Distribution of the Sample Mean

### Question Description

A normally distributed population has mean 57.7 and standard deviation 12.1

Find the probability that the mean of a sample of size 16 drawn from this population is less than 45

The sample mean is the population mean: 57.7.

The standard deviation of the sample mean (called the "standard error") is

population standard deviation / sqrt(sample size)

= 12.1 / sqrt(16)

= 3.025

So the probability that the sample mean will be less than 45 is given by the cdf of the Normal distribution with mean = 57.7 and sd = standard error = 3.025, at 45:

= Norm.cdf( x, mean, sd )

= Norm.cdf( 45, 57.7, 3.025 )

1.34435 x 10^-05

iainharlow (1041)
UC Berkeley
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