A sample of final test scores is normally distributed with a mean equal to 23 an

ID: 3307249 • Letter: A

Question

A sample of final test scores is normally distributed with a mean equal to 23 and a variance equal to 25.

Part (a)
What percentage of scores are between 18 and 28? (Round your answer to two decimal places.)

Part (b)
What raw score is the cutoff for the top 10% of scores? (Round your answer to one decimal place.)

Part (c)
What is the proportion below 16? (Round your answer to four decimal places.)

Part (d)
What is the probability of a score less than 30? (Round your answer to four decimal places.)

Solution
Mean = 23 and SD = Sqrt(Variance) = 5

a) P(18<X<28)

Z = (18-23)/5 = -1

Z = (28-23)/5 = 1

P(18<X<28) = P(X<28) - P(X<18) = 0.8413 - 0.1587 = 0.6826 or 68.26%

b). Probability is = 0.1

Z value from Z table = -1.28

cut off score is

-1.28 = (Xbar - 23)/5

-6.40 = Xbar -23

Xbar = 23-6.40 = 16.6

C). Proportion below 16 means P(X<16)

Z = (16-23)/5

Z = -7/5 = -1.4

P(X<16) = 0.0808 or 8.08%

D). P(X<30)

Z = (30-23)/5 = 7/5 = 1.4

P(X<30) = 0.9192 or 91.92%

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