Statistics Review Normal Distribution

The average number of calories in a 1.5-ounce chocolate bar is 225.  Suppose that the distribution of calories is approximately normal with a σ of 10.  Find the probability that a randomly selected chocolate bar will have between 200 and 220 calories. 

• 0.9876
• 0.3023
• 0.0098
• 0.3320

Braking distance for car on a wet surface is normally distributed with a mean of 149 ft. and a standard deviation of 5.28 ft. Find the probability that the randomly picked car will have a breaking distance more than 160 feet.

• 0.4559

• 0.0186

• 0.2244

• 2.3

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. What height represents the first quartile? (i.e. the 1st 25% of data)

• 69.37 in

• 67.59 in

• 73.12 in

• 69.12 in

A z-score tells you...

• the standard deviation of a sampling distribution.
• the original raw score on which it is based.
• if the distribution it comes from is normal.
• how many standard deviations away from the mean a score lies.

At a local high school, GPAs are normally distributed with a mean of 2.9 and standard deviation of 0.6. What GPA boundary separates the students with the highest 2.5% of GPAs from the rest of the students?

• 3.9

• 4.1

• 4.2

• 4.0

Find the area under the standard normal curve between z = -2.55 and z = 1.08. 

• 0.8545
• 0.7560
• 0.3110
• 0.2140

The mean temperature in Glens Falls for the month of February is 23 degrees with a standard deviation of 4.2 degrees. What is the z-score for a temperature of 17 degrees?

• 1.25

• 1.43

• -1.43

• -1.25

The scoring of modern IQ is such that 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

Suppose that 10th grade girls have hair lengths that are normally distributed with a mean of 10 inches and a standard deviation of 4 inches. How long would a 10th grade girl's hair have to be in order to be at the 80th percentile for length?

• 13.4 inches
• 6.6 inches
• 4.4 inches
• 14.7 inches

Suppose teenagers that attend public high schools get an average of 5.7 hours of sleep each night with a standard deviation of 1.7 hours, and that hours of sleep is a normal distribution. What is the probability that a randomly selected group of 35 high school students averages more than 6 hours of sleep each night?

• .430

• .149

• .281

• .087