To estimate the mean height μμ of male students on your campus, you will measure an SRS of students. You know from government data that heights of young men are approximately Normal with standard deviation about 2.8 inches. You want your sample mean x⎯⎯⎯x¯ to estimate μμ with an error of no more than one-half inch in
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
To estimate the mean height μμ of male students on your campus, you will measure an SRS of students. You know from government data that heights of young men are approximately Normal with standard deviation about 2.8 inches. You want your sample mean x⎯⎯⎯x¯ to estimate μμ with an error of no more than one-half inch in either direction.
(a) What standard deviation must x⎯⎯⎯x¯ have so that 95% of all samples give an x⎯⎯⎯x¯ within one-half inch of μμ? (Use the
(b) How large an SRS do you need to reduce the standard deviation of x⎯⎯⎯x¯ to the value you found in part(a)?
(a)
(b)
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