1. What area is between the mean and the z-scores of: a. 0.5 b. 0.8 c. 1.2 d. -0

Question

1. What area is between the mean and the z-scores of:

a. 0.5          b. 0.8          c. 1.2          d. -0.8          e. -2.0

2. What z-score relates to an area between the z-score and the mean of:

a. 0.2157          b. 0.3508          c. 0.4147          d. 0.1255          e. .0517

3. What is the percentile score for the following z-scores?

a. 1.0          b. -1.0          c. 1.5          d. 0.2          e. -0.8

4. What z-scores are associated with the following percentile scores?

a. 95%          b. 68%          c. 50%          d. 25%          e. 10%

5. A person with a serum cholesterol level higher than 200 mg/dL falls in a high-risk category for cardiac disease. What percentage of the population WOULD NOT be in the high-risk category, if...

a. mean = 190, sd = 10

b. mean = 175, sd = 20

c. mean = 180, sd = 10

d. mean = 190, sd = 5

e. mean = 192, sd = 4.2

6. Using the example above for a-e, what percentage of the population WOULD be in the high-risk category?

7. Assume that the mean of the I.Q. test scale is 100 and the sd is 20. How smart are you, relative to the population, if you earn a score of...

a. 105       b. 112        c. 92          d. 97         e. 124

Explanation / Answer

Since you have posted multiple questions,i am attaching answers for first three problems with all subparts

1)

z score for mean is 0

so P(z<0) =0.5

a) P(z<0.5) =0.6915

so area between z=0 and z=0.5 is 0.6915-0.5 =0.1915

b) P(z<0.8) =0.7881

so area between z=0 and z=0.8 is 0.7881-0.5 =0.2881

c) P(z<1.2) =0.8849

so area between z=0 and z=1.2 is 0.8849-0.5 =0.3849

d) P(z<-0.8) =0.2119

so area between z=-0.8 and z=0 is 0.5-0.2119 =0.2881

e) P(z<-2) =0.0228

so area between z=-2 and z=0 is 0.5-0.0228 =0.4772

2)

a) P(z<c) -P(z<0) =0.2157

P(z<c) =P(z<0) +0.2157

= 0.5+0.2157 =0.7157

z score for P=0.7157 is c=0.57

b)

P(z<c) =P(z<0) +0.0.3508

= 0.5+0.3508 =0.8508

z score for P=0.8508 is c=1.04

c) P(z<c) =P(z<0) +0.4147

= 0.5+0.4147 =0.9147

z score for P=0.9147 is c=1.37

d) P(z<c) =P(z<0) +0.1255

= 0.5+0.1255 =0.6255

z score for P=0.6255 is c=0.32

e) P(z<c) =P(z<0) +0.0517

= 0.5+0.0517 =0.5517

z score for P=0.5517 is c=0.13

3)

a) z=1

P(z<1) =0.8413 =84.13%

b) z=-1

P(z<-1) =0.1587 =15.87%

c) z=1.5

P(z<1.5) =0.9332 =93.32%

d) z=0.2

P(z<0.2) =0.5793 =57.93%

e) z=-0.8

P(z<-0.8) =0.2119 =21.19%

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