Question

A European intelligence test is designed with a mean of 220 and a standard deviation of 33 (because of the metric system, of course). The test is designed so that scores will follow a Normal model.

a. On separate paper, draw and label the distribution of scores on this test. Include the __-__-___ Rule. (The blanks mean you should know those numbers.)

b. Sandrine's score is the 65th percentile. What score did she get? (round to the nearest whole number)

c. Reynaud scores 199 on the test. What z-score is that? (round to 2 decimal places)

d. What percent of all test takers will score over 250? (as a percent, round to 1 decimal place, like 12.3%)

Answer 1

This is a normal distribution question with

a) On separate paper, draw and label the distribution of scores on this test. Include the 68-95-99.7 Rule.

b) Sandrine's score is the 65th percentile
Given in the question, p = 0.65
P(X < x) = 0.65
This implies that
P(Z < 0.3853) = 0.65
With the help of formula for z, we can say that

She got 233

c) P(x = 199.0)=?
The z-score at x = 199.0 is,


d) P(x > 250.0)=?
The z-score at x = 250.0 is,

This implies that

18.2 % of all test takers will score over 250

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