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Chapter 6: Q. 23 (page 385)

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

Short Answer

Expert verified

The value of the zscore is -1.67

Step by step solution

01

Given Information 

Given in the question that, X~N(12,6)

x=2

We have to find thezscore

02

Explanation 

Let's consider the expression X~N(12,6)

Where,

μ=12

σ=6

x=2

We can compute the zscore as follow:

z=x−μσ

Place the given values in the above equation

Then,

z=2−126

=−106

=−1.67

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Most popular questions from this chapter

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~_____(_____,_____)

Suppose that Ricardo and Anita attend different colleges. Ricardo's GPA is the same as the average GPA at his school. Anita's GPA is 0.70 standard deviations above her school average. In complete sentences, explain why each of the following statements may be false.

a. Ricardo's actual GPA is lower than Anita's actual GPA.

b. Ricardo is not passing because his z-score is zero.

c. Anita is in the 70th percentile of students at her college.

Use the following information to answer the next four exercises: X~N(54,8)

Find the probability thatx<30

In a normal distribution, x = 3 and z = 0.67. This tells you that x = 3 is ____ standard deviations to the ____ (right or left) of the mean.

The life of Sunshine CD players is normally distributed with a mean of 4.1years and a standard deviation of 1.3years. A CD player is guaranteed for three years. We are interested in the length of time a CD player lasts. Find the probability that a CD player will break down during the guarantee period.

a. Sketch the situation. Label and scale the axes. Shade the region corresponding to the probability.

b. P(0<x<____________)=___________(Use zero for the minimum value of x.)
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