Finding Data Value Given Probability

The scoring of modern IQ is such that Intelligence Quotients (IQs) have a normal distribution with a mean = 100 and a standard deviation = 15.

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

• 130

• 131

• 145

• 120

The scores on a university examination are Normally distributed with a mean of 62 and a standard deviation of 11. If the bottom 5% of students will fail the course, what is the lowest mark that a student can have and still be awarded a passing grade?

• 40

• 43

• 44

• 57

• 62

The time to complete a standardized exam is approximately Normal with a mean of 70 minutes and a standard deviation of 10 minutes. How much time should be given to complete the exam so that 80% of the students will complete the exam in the time given?

• 61.6 minutes

• 78.4 minutes

• 79.8 minutes

• 84 minutes

• 92.8 minutes

In a survey of men in the United States (ages 20-29), the mean height was 69.6 inches with a standard deviation of 3.0 inches. Find the minimum height in the top 22%.

• 69.37 in 

• 67.58 in 

• 73.12 in 

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

Scores on a certain standardized test have a mean of 500, and a standard deviation of 100. What score would you need to fall at the 84th percentile?

• 84

• 400

• 500

• 600

IQ scores are normally distributed with a mean of 100 and standard deviation 15. Find the IQ of the top 15%

• 135

• 125

• 120

• 115

Standard Normal Distribution (mean is 0 and standard deviation is 1). Find the score that separates the lowest 98% from the highest 2%.

• - 2.05

• 2.05

• -1.95

• 1.95

Find the z-score such that 30% of the standard normal curve lies to the left of z. 

• -1.88

• 0.52

• -0.52

• 1.88

A bank's loan officer rates applicants for credit. The ratings are normally distributed with a mean of 200 and a standard deviation of 50. Find, the score of the lower 60%.

• 187.5

• 212.7

• 207.8

• 211.3