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# Measurements are made on the length and width (in cm) of a ISBN: 9780073401331 38

## Solution for problem 15E Chapter 2.5

Statistics for Engineers and Scientists | 4th Edition

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Problem 15E

Measurements are made on the length and width (in cm) of a rectangular component. Because of measurement error, the measurements are random variables. Let X denote the length measurement and let Y denote the width measurement. Assume that the probability density function of X is and that the probability density function of Y is Assume that the measurements X and Y are independent.

a. Find P(X<9.98).

b. Find P(Y > 5.01).

c. Find P(X<9.98 and Y > 5.01).

d. Find μX.

e. Find μγ.

Step-by-Step Solution:

Step 1:

Let X denote the length measurement and let Y denote the width measurement. Here the probability density function of X is And the density function of Y is We have to find

P(X<9.98) P(Y> 5.01) P(X<9.98 and Y>5.01) E(X) E(Y)

Step  2:

We have to find the probability P(X<9.98)

P(X<9.98) = f(x)  dx

= =   10 [X =  10 (9.98-9.95)

= 0.3.

Therefore the probability P(X<9.98) is 0.3.

(b)  We have to find the probability that P(Y>5.01)

P(Y>5.01) = f(y) dy

= 5 dy

=   5 [y =  5 [5.1-5.01]

=  0.45

Therefore the probability P(Y>5.01)  is 0.45.

(c)   We have to find the probability that P(X<9.98 and Y>5.01)

Since the measurements X and Y are independent

P(X<9.98 and Y>5.01) = P(X<9.98) P(Y>5.01)

=  (0.3) (0.45)

= 0.135

Step 3 of 3

##### ISBN: 9780073401331

The full step-by-step solution to problem: 15E from chapter: 2.5 was answered by , our top Statistics solution expert on 06/28/17, 11:15AM. Statistics for Engineers and Scientists was written by and is associated to the ISBN: 9780073401331. The answer to “Measurements are made on the length and width (in cm) of a rectangular component. Because of measurement error, the measurements are random variables. Let X denote the length measurement and let Y denote the width measurement. Assume that the probability density function of X is and that the probability density function of Y is Assume that the measurements X and Y are independent.a. Find P(X<9.98).________________b. Find P(Y > 5.01).________________c. Find P(X<9.98 and Y > 5.01).________________d. Find ?X.________________e. Find ??.” is broken down into a number of easy to follow steps, and 79 words. Since the solution to 15E from 2.5 chapter was answered, more than 983 students have viewed the full step-by-step answer. This textbook survival guide was created for the textbook: Statistics for Engineers and Scientists , edition: 4. This full solution covers the following key subjects: Find, measurements, measurement, Density, Probability. This expansive textbook survival guide covers 153 chapters, and 2440 solutions.

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