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Chapter 10: Q. AP3.10 (page 702)

Let X represent the outcome when a fair six-sided die is rolled. For this random variable, μX=3.5and σX=1.71. If the die is rolled 100 times, what is the approximate probability that the sum is at least 375?

a. 0.0000

b.0.0017

c.0.0721

d.0.4420

e.0.9279

Short Answer

Expert verified

The probability is 0.0721

Step by step solution

01

Given Information

We have to find the probability that sum is at least 375.

02

Simplification

Population mean (μx)=3.5

Population standard deviation(σx)=1.71

Sample size (n)=100

The mean can be calculated as follows:

x-=375100=3.75

The likelihood that the sum is at least 375can be computed as follows:

P(x-≥3.75)=Px−μσn≥3.75−3.51.71100=P(Z≥1.47)=1−P(Z≤1.47)=0.0721

Thus, the required probability is0.0721.

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