a. What is the distribution of ? a - N( b. For the group of 44, find the probability that the average price is between $173 and $178. c. Find the third quartile for the average textbook price for this sample size. $ (round to the nearest cent) d. For part b), is the assumption that the distribution is normal necessary? No Yes
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.
![The average price of a college math textbook is $167, and the standard deviation is $28. Suppose that 44 textbooks are randomly chosen. Round all answers to four decimal places where possible.
a. What is the distribution of \( \overline{x} \)? \(\overline{x} \sim N(\, \_\_\_\_\_\_\_\_\_\_\_, \_\_\_\_\_\_\_\_\_\_\_ \,)\)
b. For the group of 44, find the probability that the average price is between $173 and $178. \[\_\_\_\_\_\_\_\_\_\_\_\]
c. Find the third quartile for the average textbook price for this sample size. $[\_\_\_\_\_\_\_\_\_\_\_\] (round to the nearest cent)
d. For part b), is the assumption that the distribution is normal necessary?
[ ] No
[ ] Yes](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fef4421a9-80f4-44ac-a84c-7924c290e1b7%2F5f79150f-6323-455c-82fc-1e06c890995c%2F3irb3k_processed.jpeg&w=3840&q=75)
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