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Chapter 6: Q 16 (page 385)

Suppose X ~ N(8, 1). What value of x has a z-score of 鈥�2.25?

Short Answer

Expert verified

The value of xis5.75

Step by step solution

01

Given Information

Given that, z=-2.25. And,

X~N(8,1)Where,

渭=8

蟽=1

We have to find the value ofx

02

Explanation

The value ofz-score can be calculated as below:

z=x-渭蟽

Put the provided values in the above expression. Then,

-2.25=x-81

x-8=-2.25脳1

x=-2.25+8

x=5.75

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Most popular questions from this chapter

In 2005,1,475,623students heading to college took the SAT. The distribution of scores in the math section of the SAT follows a normal distribution with mean 碌=520and standard deviation 蟽=115

  1. Calculate the z-score for an SAT score of 720. Interpret it using a complete sentence.
  2. What math SAT score is 1.5 standard deviations above the mean? What can you say about this SAT score?
  3. For 2012, the SAT math test had a mean of 514 and standard deviation 117. The ACT math test is an alternate to the SAT and is approximately normally distributed with mean 21 and standard deviation 5.3. If one person took the SAT math test and scored 700 and a second person took the ACT math test and scored 30, who did better with respect to the test they took?

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.

The 90thpercentile for recovery times is

a. 8.89

b. 7.07

c. 7.99

d. 4.32

About what percent of the x values from a normal distribution lie within two standard deviations (left and right) of the mean of that distribution?

齿词狈(鈥�4,1)

What is the median?

X~N(鈥�3,4)

Find the probability that x is between one and four.
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