Question

# A statistics teacher believes that the final exam grades for her class have a normal distribution...

 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 z-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. (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.

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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