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Chapter 6: Q. 36 (page 386)

Suppose X~N(鈥�3,1). Between what xvalues does 34.14%of the data lie?

Short Answer

Expert verified

The 34.14%of data lies between (-3.44,-2.56).

Step by step solution

01

Given Information

Given in the question that, X~N(鈥�3,1).

We have to find between what xvalues does 34.14%of the data lie.

02

Explanation 

The 34.14%is lies in the middle of the normal curve,

Therefore the portion will be divided as equal in both side.

34.14%2=17.07%

So it will be

50%鈭�17.07%=32.93%

So the value of the outside will be32.93%

Now, we need to find the z-value for the 32.93%

z0.3293=鈭�0.44(left鈭�tail)

z0.3293=0.44(right鈭�tail)

The z- score formula is

z=x鈭�渭蟽

鈭�0.44=x鈭�(鈭�3)1鈬�鈭�0.44脳1=x+3鈬�x=鈭�3鈭�0.44鈬�x=鈭�3.44

0.44=x鈭�(鈭�3)1鈬�0.44脳1=x+3鈬�x=鈭�3+0.44鈬�x=鈭�2.56

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Most popular questions from this chapter

Use the following information to answer the next four exercises:

X~N(54,8)

Find the probability thatx>56.

The systolic blood pressure (given in millimeters) of males has an approximately normal distribution with mean 碌=125and standard deviation 蟽=14. Systolic blood pressure for males follows a normal distribution.

a. Calculate the z-scores for the male systolic blood pressures 100and 150millimeters.

b. If a male friend of yours said he thought his systolic blood pressure was 2.5 standard deviations below the mean, but that he believed his blood pressure was between 100 and 150 millimeters, what would you say to him?

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.

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b. 2.41

c. 3.95

d. 6.05

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