Answered: Given the normally distributed variable…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter4: Polynomial And Rational Functions

Section4.6: Variation

Problem 37E

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Given the normally distributed variable X with
mean 18 and standard deviation 2.5, find
(a) P(X <15);
(b) the value of k such that P(X <k) = 0.2236;
(c) the value of k such that P(X >k) = 0.1814;
(d) P(17 < X < 21).
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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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Given the normally distributed variable X with mean 18 and standard deviation 2.5, find (a) P(X <15); (b) the value of k such that P(X k) = 0.1814; (d) P(17 < X < 21).