Answered: Find the probability that the student’s…

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.4: Distributions Of Data

Problem 19PFA

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Exercise #2
Use the Using Excel for Normal Probabilities instructions for the following.
In a recent year, the ACT scores for high school students with an A or B grade point average were
normally distributed with a mean of 24.2 and a standard deviation of 4.2. A student with an A or B
average who took the ACT during this time is selected.

1. Find the probability that the student’s ACT score is less than 20.

2. Find the probability that the student’s ACT score is greater than 31.

3. Find the probability that the student’s ACT score is between 25 and 32.

4. Find the probability that in a sample of size 100, the mean ACT score is between 25 and 32.

5. Find the cutoffs for the middle 90% for the mean ACT scores in a sample of size 100.

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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