Question

For the following, the data set has a mean of ? = 100 and a standard deviation of ? = 20.   Find the following areas under the curve for the region that is:

1) Less than 100

2) Greater than 160

For the following, scores on a psychology exam were normally distributed with a mean of 67 and a standard deviation of 8. Find the following:

1) What percentage of scores were below 83?

2) If 500 students took the exam, approximately how many students scored below 75?

Answer 1

1)

This is a normal distribution question with

a) P(x < 100.0)=?

The z-score at x = 100.0 is,

z = 0.0

This implies that

b) P(x > 160.0)=?

The z-score at x = 160.0 is,

z = 3.0

This implies that

P(x > 160.0) = P(z > 3.0) = 1 - 0.9986501019683699

2)

This is a normal distribution question with

a) P(x < 83.0)=?

The z-score at x = 83.0 is,

z = 2.0

This implies that

b)

Sample size (n) = 500

Since we know that

a) P(x < 75.0)=?

The z-score at x = 75.0 is,

z = 22.3589

This implies that

PS: you have to refer z score table to find the final probabilities.

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