a. What is the distribution of ? T - N( b. For the group of 14, find the probability that the average number of friends is more than 94. c. Find the first quartile for the average number of Facebook friends.
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.
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a.
Central limit theorem:
Based on central limit theorem, if the population is normally distributed then the sampling distribution is also normally distributed regardless of the sample size. If there is no information about the population, for sufficiently large sample size n≥30 sampling distribution of sample mean has the normal distribution.
Let be the average number of Facebook friends users which follows normal distribution. The mean is 111 and standard deviation is 59. That is, .
The mean of the sampling distribution is,
The standard deviation of the sampling distribution is,
Thus, the distribution of is .
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