The average price of a college math textbook is $175 and the standard deviation is $23. Suppose that 14 textbooks are randomly chosen. Round all answers to 4 decimal places where possible. a. What is the distribution of ¯ x ? ¯ x ~ N b. or the group of 14, find the probability that the average price is between $170 and $179. c. Find the third quartile for the average textbook price for this sample size
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.
- Sampling Distribution of a Normal Variable :
Given a random variable X. Suppose that the population distribution of X is known to be normal, with mean µ and
variance σ2 , that is, X ~ N(µ, σ). Then, for any sample size n, it follows that the sampling distribution of is normal,
with mean µ and variance σ2/n , that is,
is called the “standard error of the mean,” denoted SEM, or more simply, s.e.
The corresponding Z-score transformation formula is
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