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Chapter 6: Q. 49 (page 387)

If the area to the right of x in a normal distribution is 0.543, what is the area to the left ofx?

Short Answer

Expert verified

The area to the left ofxis0.457

Step by step solution

01

Given Information

Given in the question that, If the area to the right of xin a normal distribution is0.543,

We have to find the right of thex

02

Explanation

From the information given in the question, we can represent the probability statement as P(x>x)=0.543

Therefore, the area to left of xcan be computed as follow:

P(X>x)=1−P(X<x)

0.543=1−P(X<x)

P(X<x)=1−0.543

=0.457

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Most popular questions from this chapter

Is X~N(0,1) a standardized normal distribution? Why or why not?

In 2012, 1,664,479 students took the SAT exam. The distribution of scores in the verbal section of the SAT had a mean µ=496 and a standard deviation σ=114. Let X = a SAT exam verbal section score in 2012. Then X~N(496,114). Find the z-scores for x1=325 andx2=366.21. Interpret each z-score. What can you say about x1=325 and x2=366.21 as they compare to their respective means and standard deviations ?

The length of time to find it takes to find a parking space at 9 A.M. follows a normal distribution with a mean of five minutes and a standard deviation of two minutes. If the mean is significantly greater than the standard deviation, which of the following statements is true?

I. The data cannot follow the uniform distribution.

II. The data cannot follow the exponential distribution..

III. The data cannot follow the normal distribution.

a. I only

b. II only

c. III only

d. I, II, and III

The percent of fat calories that a person in America consumes each day is normally distributed with a mean of about 36 and a standard deviation of 10 . Suppose that one individual is randomly chosen. LetX=percent of fat calories.

a. X~----------

b. Find the probability that the percent of fat calories a person consumes is more than 40 . Graph the situation. Shade in the area to be determined.

c. Find the maximum number for the lower quarter of percent of fat calories. Sketch the graph and write the probability statement.

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