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Distribution Problems

Authored by Anthony Clark

Mathematics

12th Grade

Distribution Problems
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10 questions

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1.

MULTIPLE CHOICE QUESTION

1 min • 1 pt

What's the probability of x < 13 for a normal distribution ?

(Mean = 20, Standard dev = 6.5)

0.3529

0.1471

0.8529

0.6471

2.

MULTIPLE CHOICE QUESTION

1 min • 1 pt

The scoring of modern IQ is such that Intelligence Quotients (IQs) have a normal distribution of μ= 100 and 𝞂 = 15.


Mensa International is a non-profit organization that accepts only people with IQ score within the top 2%. What level of IQ qualifies one to be a member of Mensa?

115

130.75

145

120

3.

MULTIPLE CHOICE QUESTION

1 min • 1 pt

The distances male long jumpers for State College jump are approximately normal with a mean of 263 inches and a standard deviation of 14 inches. Suppose a male long jumper's jump ranked in the 75th percentile. How long was his jump?

0.67 inch

263 inches

272.44 inches

277.25 inches

4.

MULTIPLE CHOICE QUESTION

1 min • 1 pt

The 40 yards sprint times for a soccer team are found to be normally distributed with a mean of 5.2 seconds and a standard deviation of 0.3 seconds. What is the z-score for a player who runs a time of 5.6 seconds?

-1.33

1.33

0.88

1.02

5.

MULTIPLE CHOICE QUESTION

1 min • 1 pt

Find the z-score with 20% of observations falling above it.

z=-0.84

z=1.84

z=-1.84

z=0.84

6.

MULTIPLE CHOICE QUESTION

1 min • 1 pt

Z-score of 2.5 on an IQ test is considered a genius (mean=100, SD=16). What score makes someone a genius? Hint: Area to the left (below) = Score

89.2

130

99.38

140

7.

MULTIPLE CHOICE QUESTION

1 min • 1 pt

In a certain game, a player can win $50 with a probability of 0.3, win $100 with a probability of 0.2, and lose $20 with a probability of 0.5. What is the expected value of the game?

Expected value = (50 * 0.2) + (100 * 0.5) + (-20 * 0.3) = 10 + 50 - 6 = $54

Expected value = (50 * 0.4) + (100 * 0.1) + (-20 * 0.6) = 20 + 10 - 12 = $18

Expected value = (50 * 0.3) + (100 * 0.2) + (-20 * 0.5) = 15 + 20 - 10 = $25

Expected value = (50 * 0.5) + (100 * 0.3) + (-20 * 0.2) = 25 + 30 - 4 = $51

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