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Chapter 6: Q 19 (page 385)

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

Short Answer

Expert verified

The value of x is 1

Step by step solution

01

Given Information

Given thatX~N(4,2)

We have to find the value of x 1.5 standard deviations to the left of the mean

02

Explanation

The value of z-score can be calculated as below:

z=x-渭蟽

Put the provided values in the above expression. Then,

-1.5=x-42

x-4=-1.5脳2

x=-3+4

x=1

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Most popular questions from this chapter

Jerome averages 16 points a game with a standard deviation of four points. X~N(16,4). Suppose Jerome scores ten points in a game. The z鈥搒core when x=10 is 鈥�1.5. This score tells you that x=10 is _____ standard deviations to the ______(right or left) of the mean______(What is the mean?).

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.

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.

A company manufactures rubber balls. The mean diameter of a ball is 12cmwith a standard deviation of 0.2 cm. Define the random variable Xin words. X=______________.

X~N(3,5)蟽=____________
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