Question

Exam grades: Scores on a statistics final in a large class were normally distributed with a mean of 71 and a standard deviation of 8. Use the TI-84 PLUS calculator to answer the following. Round the answers to at least two decimals. ol. (a) Find the 47th percentile of the scores. (b) Find the 65th percentile of the scores. (c) The instructor wants to give an A to the students whose scores were in the top 12% of the class. What is the minimum score needed to get an A? (d) Between what two values are the middle 62% of the scores? (Enter the smaller number in the first box.)

Answer 1

A.

P(Z<z) = 0.47

So using normal table:

z = -0.075

(x-mean)/std. deviation = -0.075

x = 71 - 0.075*8

= 70.4

B.

P(Z<z) = 0.65

So using normal table:

z = 0.385

(x-mean)/std. deviation = 0.385

x = 71 + 0.385*8

= 74.08

C.

P(Z>z) = 0.12

z = 1.175

(x-mean)/std. deviation = 1.175

x = 71 + 1.175*8

= 80.4

D.

P(-z<Z<z) = 0.62

i.e. z = $\pm$ 0.878

So,

71 - 0.878*8 x < 71 + 0.878*8

63.976 < 78.024

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