The Sampling Distribution of the Sample Mean

Statistics
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A normally distributed population has mean 57.7 and standard deviation 12.1

Find the probability that a single randomly selected element X of the population is less than 45

Mar 10th, 2015

The probability that the sampled element will be less than 45 is given by the normal distribution cdf at 45:

= Norm.cdf( x, mean, sd )

= Norm.cdf( 45, 57.7, 12.1 )

= 0.147


(This is because the cdf of the distribution gives you the total probability up to that point, i.e. the area under the distribution curve to the left of whatever x is)

Mar 10th, 2015

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