5.3. Applications of the Normal Distribution http://www.ck12.org
Unknown Mean or Standard Deviation
Example:
For a normally distributed random variable,σ= 4. 5 ,x=20, andp=.05, Estimateμ
Solution:
First draw a sketch:
Remember that about 95% of the data is within 2 standard deviations of the mean. This would leave 2.5% of the
data in the lower tail, so our 5% value must be less than 9 units from the mean.
Because we do not know the mean, we have to use the standard normal curve and calculate az−score using the
invNorm command. The result(− 1. 645 )confirms the prediction that the value should be less than 2 standard
deviations from the mean.