Distribution Problems

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

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

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

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

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

• z=-0.84

• z=1.84

• z=-1.84

• z=0.84

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

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

A company finds that 20% of the products it manufactures are defective. If 5 products are randomly selected, what is the probability that at least 2 of them are defective?

• 0.2345

• 0.9184

• 0.7500

• 0.5000

If the probability distribution table for a random variable X is given by: X | 1 | 2 | 3 | 4 | 5, P(X) | 0.1 | 0.2 | 0.3 | 0.2 | 0.2, what is the expected value of X?

• 2.8

• 4.0

• 3.2

• 1.5

If the probability distribution table for a random variable Y is given by: Y | 1 | 2 | 3 | 4, P(Y) | 0.2 | 0.3 | 0.4 | 0.1, what is the variance of Y?

• 0.81

• 0.25

• 1.5

• 0.5