The cost of textbooks is normally distributed with a mean of $203. You do not know the population standard deviation, but you know the sample standard deviation is $48. What is the probability that from a sample of 4 textbooks, their average cost will be less than $238? (Report answer accurate to three decimal places.)
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.
Solution:
Let X be the cost of textbook.
From the given information, x-bar=$203, s=$48 and n=4.
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