Records of a university (collected over many years) show that on the average 74 percent of all incoming fresh-men have I.Q.’s of at least 115. Of course, the percentage varies somewhat from year to year, and this variation is measured by a standard deviation of 3 percent. If a sam-ple check of 30 freshmen entering the university in 2003 showed that only 18 of them have I.Q.’s of at least 115,estimate the true proportion of students with I.Q.’s of atleast 115 in that freshman class using(a) only the prior information;(b) only the direct information; (c) the result of Exercise 74 to combine the prior infor-mation with the direct information.
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.
Records of a university (collected over many years)
show that on the average 74 percent of all incoming fresh-
men have I.Q.’s of at least 115. Of course, the percentage
varies somewhat from year to year, and this variation is
measured by a standard deviation of 3 percent. If a sam-
ple check of 30 freshmen entering the university in 2003
showed that only 18 of them have I.Q.’s of at least 115,
estimate the true proportion of students with I.Q.’s of at
least 115 in that freshman class using
(a) only the prior information;
(b) only the direct information;
(c) the result of Exercise 74 to combine the prior infor-
mation with the direct information.
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