Question

The scores on a standardized test are normally distributed with a standard deviation of 75. The z score of a student who scored 662.5 was 1.5. If 300 students took the test, how many scored less than 475?

Answer 1

Answer: 48

This value is approximate.

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Step-by-step explanation:

• mu = population mean = unknown for now
• sigma = population standard deviation = 75
• x = score on the test

We need to determine mu.

We'll use the fact x = 662.5 pairs up with z = 1.5

z = (x - mu)/sigma

1.5 = (662.5 - mu)/75

1.5*75 = 662.5 - mu

112.5 = 662.5 - mu

112.5 + mu = 662.5

mu = 662.5 - 112.5

mu = 550

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Then compute the z score when x = 475

z = (x - mu)/sigma

z = (x - 550)/75

z = (475 - 550)/75

z = -1

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Use a Z table to determine that

P(Z < -1) = 0.15866

which is approximate.

About 15.866% of the 300 students scored less than 475.

0.15866*300 = 47.598 which rounds to 48 and it is the final answer.