Explanation Given information: X is normally distributed with mean μ = 40 and σ = 5 . Calculation: Given: μ = 40 and σ = 5 We know that probability density satisfies ∫ − ∞ ∞ P ( x ) = 1 . Thus, P ( X ≤ 45 ) + P ( X ≥ 45 ) = 1 and P ( X ≥ 45 ) = 1 − P ( X ≤ 45 ) . Now from theorem 1, we know that P ( X ≤ b ) = F ( b − μ σ ) To determine (b) To calculate: The probability P ( 0 ≤ X ≤ 40 ) .

3rd Edition

ISBN: 9781464125263

Author: Jon Rogawski, Colin Adams

Publisher: W.H. Freeman & Co

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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.

Chapter 8, Problem 73CRE

To determine

(a)

To calculate:

The probability P(X≥45).

To determine

(b)

To calculate:

The probability P(0≤X≤40).

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Chapter 8, Problem 72CRE

Chapter 8, Problem 74CRE

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Chapter 8 Solutions

Calculus - Standalone book

Ch. 8.1 - Prob. 1PQ Ch. 8.1 - Prob. 2PQ Ch. 8.1 - Prob. 3PQ Ch. 8.1 - Prob. 1E Ch. 8.1 - Prob. 2E Ch. 8.1 - Prob. 3E Ch. 8.1 - Prob. 4E Ch. 8.1 - Prob. 5E Ch. 8.1 - Prob. 6E Ch. 8.1 - Prob. 7E

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(a) To calculate: The probability P ( X ≥ 45 ) .

Solution Summary: The author calculates the probability P(Xge 45) and sigma =5.

Concept explainers

Videos

(a)

To calculate:

The probability P(X≥45).

(b)

To calculate:

The probability P(0≤X≤40).

Want to see the full answer?

Chapter 8 Solutions

(a) To calculate: The probability P ( X ≥ 45 ) .

Solution Summary: The author calculates the probability P(Xge 45) and sigma =5.

Concept explainers

Videos

(a) To calculate: The probability P(X≥45).

(b) To calculate: The probability P(0≤X≤40).

Want to see the full answer?

Chapter 8 Solutions

(a)

To calculate:

The probability P(X≥45).

(b)

To calculate:

The probability P(0≤X≤40).