Question

A statistics teacher believes that the final exam grades for her class have a normal distribution with a mean of 80 and a standard deviation of 8. Answer the following: | ||||

(a) |
Determine the -score for a person from
this population that has a test score of 66. Then find the
z-score for someone whose test score is
95.z |
|||

(b) | If
x represents a possible test score from this population,
find P(x > 87). |
|||

(c) | Find P(79
< x < 89) and write a sentence for
the interpretation of this value. |
|||

(d) | The top 10% of all people in this group have test scores high enough to earn an A. Determine the test score which is high enough to earn an A. | |||

Answer #1

Given that, mean = 80 and

standard deviation = 8

a) We want to find, z-score for test scores of 66 and 95

For x = 66

z = (66 - 80)/8 = **-1.75**

For x = 95

z = (95 - 80)/8 = **1.875**

b)

=> P(X > 87) = 0.1894

c)

The probability that exam grade is between 79 and 89 is 0.4225

d) We want to find, the value of x such that, P(X > x) = 0.10

Test score = 90.24

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