Math Problem Statement

In a recent​ year, the scores for the reading portion of a test were normally​ distributed, with a mean of 21.5 and a standard deviation of 5.3. Complete parts​ (a) through​ (d) below. Question content area bottom Part 1 ​(a) Find the probability that a randomly selected high school student who took the reading portion of the test has a score that is less than 17. The probability of a student scoring less than 17 is    ​(Round to four decimal places as​ needed.) Part 2 ​(b) Find the probability that a randomly selected high school student who took the reading portion of the test has a score that is between 14.1 and 28.9. The probability of a student scoring between 14.1 and 28.9 is   

​(Round to four decimal places as​ needed.)

Solution

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Math Problem Analysis

Mathematical Concepts

Normal Distribution
Z-scores
Probability

Formulas

Z = (X - μ) / σ

Theorems

Standard Normal Distribution

Suitable Grade Level

Grades 10-12