AP Stats Finding Values of a Normally Distributed Variable

The daily total sales (excluding Saturday) at a small restaurant has a probability distribution that is approximately Normal with a mean of μ = $530 and a standard deviation of σ = $120. The probability the sales will exceed $700 on a given day is approximately

• 0.9222

• 0.5578

• 0.0778

• 0.0125

The weight of a medium-sized orange selected at random from a large bin of oranges at a local supermarket is a random variable with mean μ = 12 ounces and standard deviation σ = 1.2 ounces. Suppose we independently select two oranges at random from the bin. The difference in the weights of the two oranges (the weight of the first orange minus the weight of the second orange) is a random variable with a standard deviation equal to:

• 0 ounces

• 1.50 ounces

• 1.70 ounces

• 2.40 ounces

In a normal distribution, what percent of the values lie above the mean?

• 13.5%

• 34%

• 50%

• 68%

2000 freshmen at State Univ. took a Biology test. The scores were distributed normally with μ=70 and σ=5. What percent of scores are between 65 and 75?

• 34%

• 50%

• 68%

• 81.5%

• A
• B
• C
• D

• A

• B

• C

• D

• E

ASSUME THE GIVEN DISTRIBUTION IS NORMAL.

• A

• B

• C

• D

• E

2000 freshmen at State Univ. took a Biology test. The scores were distributed normally with μ=70 and σ=5.

What percent of scores are greater than 75?

• 2.35%

• 2.5%

• 16%

• 13.5%

2000 freshmen at State Univ. took a Biology test. The scores were distributed normally with μ=70 and σ=5. Approximately how many students scored between 60 and 80?

• 95

• 100

• 1900

• 1950

500 juniors at Central High School took the ACT last year. The scores were distributed normally with μ=24 and σ=4.

What ACT score is 3 standard deviations below the mean?

• 12

• 16

• 20

• 21