Suppose that random variable X has a normal distribution with mean μ standard deviation σ = 4, so that X - N(10,4). Find: a) a x0.05 such that Pr(X ≤ 0.05) = 0.05, x0.05 = b) a x 0.975 such that Pr(|X|X0.975) = 0.95, X0.975 = = 10 and c) the 75th percentile of the distribution of X. That is, the value X0.75 such that Pr(Xx0.75) 0.75. X0.75 +0.75= =

Suppose that random variable X has a normal distribution with mean μ standard deviation σ = 4, so that X - N(10,4). Find: a) a x0.05 such that Pr(X ≤ 0.05) = 0.05, x0.05 = b) a x 0.975 such that Pr(|X|X0.975) = 0.95, X0.975 = = 10 and c) the 75th percentile of the distribution of X. That is, the value X0.75 such that Pr(Xx0.75) 0.75. X0.75 +0.75= =

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section10.8: Probability

Problem 31E

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Question

Suppose that random variable X has a normal distribution with mean μ = 10 and standard deviation σ = 4, so that (10,4) XN. Find:

Suppose that random variable X has a normal distribution with mean μ
standard deviation σ = 4, so that X - N(10,4). Find:
a) a x0.05 such that Pr(X ≤ 0.05) = 0.05,
x0.05 =
b) a x 0.975 such that Pr(|X|X0.975) = 0.95,
X0.975
=
= 10 and
c) the 75th percentile of the distribution of X. That is, the value X0.75 such that
Pr(Xx0.75) 0.75.
X0.75 +0.75=
=

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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