40 lb/in2The tensile strength of paper is modeled by a

Chapter 4, Problem 193SE

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QUESTION:

The tensile strength of paper is modeled by a normal distribution with a mean of 35 pounds per square inch and a standard deviation of 2 pounds per square inch.

(a) What is the probability that the strength of a sample is less than ?

(b) If the specifications require the tensile strength to exceed , what proportion of the samples is scrapped?

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QUESTION:

The tensile strength of paper is modeled by a normal distribution with a mean of 35 pounds per square inch and a standard deviation of 2 pounds per square inch.

(a) What is the probability that the strength of a sample is less than ?

(b) If the specifications require the tensile strength to exceed , what proportion of the samples is scrapped?

ANSWER:

Step 1 of 4

Given,

The Mean,

The standard deviation,  

Suppose that X is a normal random variable with mean  and variance . Then,

where Z is a standard normal random variable, and

is the z-value obtained by standardizing X. The probability is obtained by using Appendix Table III.

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