To estimate the mean score of those who took the Medical College Admission Test on your campus, you will obtain the scores of an SRS of students. From published information you know that the scores are approximately Normal with standard deviation about 6.4. You want your sample mean x to estimate with an error of no more than 1 point in either direction. (a) What standard deviation must x have so that 99.7% of all samples give an x within 1 point of ? (Use the 68–95–99.7 rule.) (b) How large an SRS do you need in order to reduce the standard deviation of x to the value you found in part (a)?
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
SRS of students. From published information you know that
the scores are approximately Normal with standard deviation
about 6.4. You want your sample mean x to estimate with
an error of no more than 1 point in either direction.
(a) What standard deviation must x have so that 99.7% of all
samples give an x within 1 point of ? (Use the 68–95–99.7
rule.)
(b) How large an SRS do you need in order to reduce the
standard deviation of x to the value you found in part (a)?
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