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Chapter 6: Q. 54 (page 387)

X~N(6,2)

Find the probability that xis between three and nine.

Short Answer

Expert verified

The probability that X is between 3 and 9is equal to0.87.

Step by step solution

01

Given Information

Let variable Xhas normal allocation with mean 渭and variance 蟽2.

Then probability density operation is determined by:

f(x)=12蟺蟽e-12(x-渭)2蟽2,x鈭�R

02

Explanation

Let Xhas normal allocation with mean 6 and normal deviation 2,X~N6,22.

Now we require to find the probability that Xis between 3and 9.

We have the following:

P(3<X<9)=鈭�39f(x)dx

Substitute the given expression,

=鈭�3912蟺2e-12(x-6)222dx

=鈭�3612蟺2e-12x-622dx

u=x-62,du=12dx

03

Calculation

Substitute the given expression,

=鈭�-1.51.512蟺e-u22du

=NORMSDIST(1.5)-NORMSDIST(-1.5)

Substract the given expression,

=0.93-0.07

We get,

=0.87.

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Most popular questions from this chapter

The length of time it takes to find a parking space at 9 A.M. follows a normal distribution with a mean of five minutes and a standard deviation of two minutes.

Based upon the given information and numerically justified, would you be surprised if it took less than one minute to find a parking space?

a. Yes

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Suppose X ~ N(12, 6). What is the z-score of x = 2?

In China, four-year-olds average three hours a day unsupervised. Most of the unsupervised children live in rural areas, considered safe. Suppose that the standard deviation is 1.5hours and the amount of time spent alone is normally distributed. We randomly select one Chinese four-year-old living in a rural area. We are interested in the amount of time the child spends alone per day.

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