Suppose the annual employer 401(k) cost per participant is normally distributed with a standard deviation of $625, but the mean is unknown. (a) If 73.89% of such costs are greater than $1,700, what is the mean annual employer 401(k) cost per participant? (b) Suppose the mean annual employer 401(k) cost per participant is $2,258 and the standard deviation is $625. If such costs are normally distributed, 31.56% of the costs are greater than what value?
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.
Suppose the annual employer 401(k) cost per participant is
(a) If 73.89% of such costs are greater than $1,700, what is the mean annual employer 401(k) cost per participant?
(b) Suppose the mean annual employer 401(k) cost per participant is $2,258 and the standard deviation is $625. If such costs are normally distributed, 31.56% of the costs are greater than what value?
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