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Chapter 6: Q 18 (page 385)

Suppose X ~ N(2, 3). What value of x has a z-score of 鈥�0.67?

Short Answer

Expert verified

The value of x is-0.01

Step by step solution

01

Ste 1 Given Information

Given that

z=-0.67And,

X~N(2,3)Where,

渭=2

蟽=3

02

Explanation

The z-score is defined as below:

z=x-渭蟽

To find the x-value corresponding to z=-0.67,put the provided values in the above expression. Then,

-0.67=x-23

x-2=-0.67脳3

x=-2.01+2

x=-0.01

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Most popular questions from this chapter

Suppose X ~ N(4, 2). What value of x is 1.5 standard deviations to the left of the mean?

About what percent ofx values lie between the mean and three standard deviations?

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

The golf scores for a school team were normally distributed with a mean of 68and a standard deviation of three.

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Suppose that the distance of fly balls hit to the outfield (in baseball) is normally distributed with a mean of 250 feet and a standard deviation of 50 feet.

a. If X=distance in feet is for a fly ball, then X~

b. If one fly ball is randomly chosen from this distribution, what is the probability that this ball will travel fewer than 220 feet? Sketch the graph. Scale the horizontal axis XShade the region corresponding to the probability. Find the probability.

c. Find the 80ithpercentile of the distribution of fly balls. Sketch the graph, and write the probability statement.

A The distance of fly balls hit to the outfield in baseball is denoted as: N~N(250,50)

B: The probability that a randomly selected fly ball traveled fewer than 220 feet is given by P(x<220)=0.2743
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