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An experimental work to measure the strength of a particular steel was conducted. It was found that the strength of the metal is normally distributed with mean 70 and variance 9. (a) What is the probability of randomly selecting a satisfactory sample given that the satisfactory condition is when the strength value is within 68 and 74? (b) If the range of satisfactory for metal strength is (70 – x, 70 + x). What is the value of x that would give a 95% satisfactory strength of all the samples. (c) If someone selected ten (10) independently samples, what is the probability that at most seven (7) samples will have strength that is less than 74?

An experimental work to measure the strength of a particular steel was conducted. It was found that the strength of the metal is normally distributed with mean 70 and variance 9. (a) What is the probability of randomly selecting a satisfactory sample given that the satisfactory condition is when the strength value is within 68 and 74? (b) If the range of satisfactory for metal strength is (70 – x, 70 + x). What is the value of x that would give a 95% satisfactory strength of all the samples. (c) If someone selected ten (10) independently samples, what is the probability that at most seven (7) samples will have strength that is less than 74?

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.4: Distributions Of Data
Problem 19PFA
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An experimental work to measure the strength of a particular steel was conducted. It was found that the strength of the metal is normally distributed with mean 70 and variance 9. (a) What is the probability of randomly selecting a satisfactory sample given that the satisfactory condition is when the strength value is within 68 and 74? (b) If the range of satisfactory for metal strength is (70 – x, 70 + x). What is the value of x that would give a 95% satisfactory strength of all the samples. (c) If someone selected ten (10) independently samples, what is the probability that at most seven (7) samples will have strength that is less than 74?
Transcribed Image Text:An experimental work to measure the strength of a particular steel was conducted. It was found that the strength of the metal is normally distributed with mean 70 and variance 9. (a) What is the probability of randomly selecting a satisfactory sample given that the satisfactory condition is when the strength value is within 68 and 74? (b) If the range of satisfactory for metal strength is (70 – x, 70 + x). What is the value of x that would give a 95% satisfactory strength of all the samples. (c) If someone selected ten (10) independently samples, what is the probability that at most seven (7) samples will have strength that is less than 74?
Expert Solution
Step 1

Given:

μ=70σ2=9σ=σ2σ=3

Step 2

Part a.

x = strength value is between 68 and 74

Using Z score we get,

p(68<x<74)=P68-703<x-μσ<74-703                        =P(-0.6667<Z<1.3333)

Using Z table or excel command =NORMSDIST(-0.6667) and =NORMSDIST(1.3333)  we get,

P(Z<-0.6667)=0.2525P(Z<1.3333)=0.9088P(-0.6667<Z<1.3333)=0.9088-0.2525                                             =0.6563

When strength is between 68 and 74 the probability is 0.6563

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