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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 μand variance σ2.

Then probability density operation is determined by:

f(x)=12πσe-12(x-μ)2σ2,x∈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)=∫39f(x)dx

Substitute the given expression,

=∫3912π2e-12(x-6)222dx

=∫3612π2e-12x-622dx

u=x-62,du=12dx

03

Calculation

Substitute the given expression,

=∫-1.51.512πe-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

IQ is normally distributed with a mean of 100and a standard deviation of 15. Suppose one individual is randomly chosen. Let X=IQof an individual.

a. X~_____(_____,_____)

b. Find the probability that the person has an IQ greater than 120. Include a sketch of the graph, and write a probability statement

c. MENSA is an organization whose members have the top 2%of all IQs. Find the minimum IQ needed to qualify for the MENSA organization. Sketch the graph, and write the probability statement.

d. The middle 50%of IQs fall between what two values? Sketch the graph and write the probability statement.

The patient recovery time from a particular surgical procedure is normally distributed with a mean of 5.3days and a standard deviation of 2.1days.

What is the median recovery time?

a. 2.7

b. 5.3

c. 7.4

d. 2.1

a. Suppose a 15 to 18-year-old male from Chile was 176cm tall from 2009to 2010. The z-score when x=176 cm isz= _______. This z-score tells you that x=176cm is ________ standard deviations to the ________ (right or left) of the mean _____ (What is the mean?). b. Suppose that the height of a 15 to 18-year-old male from Chile from2009 to 2010 has a z-score of z=–2. What is the male’s height? The z-score(z=–2) tells you that the male’s height is ________ standard deviations to the __________ (right or left) of the mean.

Use the following information to answer the next two exercises: The life of Sunshine CD players is normally distributed with mean of 4.1 years and a standard deviation of 1.3 years. A CD player is guaranteed for three years. We are interested in the length of time a CD player lasts.

X~_____(_____,_____)

If the area to the left of xin a normal distribution is 0.123, what is the area to the right of x?
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