Probabilities Using the Normal Distribution

In Standford, CA, cars were traveling at a mean speed of 23.84 mph, with a standard deviation of 3.56 mph. One car's z-score was +3.2. How fast was that car going?

• 72.728 mph

• 12.448 mph

• 35.232 mph

• 32.563 mph

Answer explanation

μ = 350 , σ = 20 , find P(X > 400)

• 0.0062

• 0.9938

• 0.4013

• 0.5987

Between what two standard deviations of a normal distribution contain 68% of the data?

• one below and one above

• two below and two above

• two below and zero

• zero and two above

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

Find the z-score such that 44% of the standard normal curve lies to the right of z. 

• -0.15

• -1.71

• 1.71

• 0.15

Fernando is 60 inches tall. The average height for his age and gender is 68 with a standard deviation of 10 inches. What percent of his peers are shorter than him?

• 46.81%

• 8%

• 78.81%

• 21.19%

The mean GPA of students in a course at UCDavis is 3.2 with a standard deviation of 0.3. What percent of students in the course have a GPA between 2.9 and 3.8? 

• 81.85%

• 47.5%

• 68%

• 95%

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 mean temperature in Glens Falls for the month of February is 23 degrees with a standard deviation of 4.2 degrees. Approximately what percent of days in February will be between 14.6 and 31.4 degrees?

• 68%

• 50%

• 99.7%

• 95%