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Chapter 6: Q. 48 (page 387)

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

Short Answer

Expert verified

The area to the right of thexis0.877

Step by step solution

01

Given Information

Given in the question that, the area to the left of xin a normal distribution is 0.123

We have to find the area to the right of thex

02

Explanation

Consider the information given in the question,

The area to the left of xcan be represented in probability statement as P(X<x)=0.123

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

P(X>x)=1−P(X<x)

=1−0.123

=0.877

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Most popular questions from this chapter

Suppose X~N(15,3). Between what xvalues does 68.27%of the data lie? The range of xvalues is centered at the mean of the distribution (i.e., 15).

Use the following information to answer the next four exercises:

X~N(54,8)

Find the probability thatx>56.

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

Suppose X ~ N(9, 3). What is the z-score of x = 9?

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 µ=520and standard deviation σ=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?
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