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Chapter 6: Q. 28 (page 385)

In a normal distribution, x = 鈥�2 and z = 6. This tells you that x = 鈥�2 is ____ standard deviations to the ____ (right or left) of the mean.

Short Answer

Expert verified

In a normal distribution, x=鈥�2and z=6.This tells you that x=鈥�2is 6standard deviations to the right of the mean.

Step by step solution

01

Given Information

Given in the question that, In a normal distribution, x=鈥�2andz=6.

We have to fill the blanks with correct answer.

02

Explanation 

A zscore means a numerical size that represents a value's association to the mean of a set of values.

By using the zscore it can be calculate that how many standard deviations, the value of xwill lie below (left) or above (right) the mean of the distribution.

From the information given in the question, we observe that x=鈥�2andz=6.

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Most popular questions from this chapter

What is the z-score of x= 鈥�2, if it is 2.78 standard deviations to the right of the mean?

The length of time 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.

Seventy percent of the time, it takes more than how many minutes to find a parking space?

a. 1.24

b. 2.41

c. 3.95

d. 6.05

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).

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?

In 2012, 1,664,479 students took the SAT exam. The distribution of scores in the verbal section of the SAT had a mean 碌=496 and a standard deviation 蟽=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 ?
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