Activì ty TimeName:Grade & Sec:Activity #5: Applications of Normal distributionSolve the following.1. In a population of high school students' algebra scores, the mean is 64 and thestandard deviation is 6. Find the z values that corresponds to a score x = 81. (5points)2. In a certain university, the students were informed that they need a grade in the top 8%of the engineering students to get a scholarship for the next semester. In thestandardization of the test, the mean was 76 and the standard deviation is 14. Assumingthat the grade is normally distributed, what must be the minimum grade to obtain thescholarship grant. (5points)3. The average loan of an employee is Php18,200. If the debt is normally distributed witha standard deviation of Php6,150, find the probabilities;a. that the employee owes more than Php20,000. (5points)b. that the employee owes between Php10,000 and Php25,000. (5points)

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Description: Activì ty TimeName:Grade & Sec:Activity #5: Applications of Normal distributionSolve the following.1. In a population of high school students' algebra scores, the mean is 64 and thestandard deviation is 6. Find the z values that corresponds to a sco

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1. In a population of high school students' algebra scores, the mean is 64 and the standard deviation is 6. Find the z values that corresponds to a score x = 81. (5points)

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Concept explainers

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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Question

Activì ty Time
Name:
Grade & Sec:
Activity #5: Applications of Normal distribution
Solve the following.
1. In a population of high school students' algebra scores, the mean is 64 and the
standard deviation is 6. Find the z values that corresponds to a score x = 81. (5points)
2. In a certain university, the students were informed that they need a grade in the top 8%
of the engineering students to get a scholarship for the next semester. In the
standardization of the test, the mean was 76 and the standard deviation is 14. Assuming
that the grade is normally distributed, what must be the minimum grade to obtain the
scholarship grant. (5points)
3. The average loan of an employee is Php18,200. If the debt is normally distributed with
a standard deviation of Php6,150, find the probabilities;
a. that the employee owes more than Php20,000. (5points)
b. that the employee owes between Php10,000 and Php25,000. (5points)

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