AP Stats Probability Using Normal Distribution

• A
• B
• C
• D

• A

• B

• C

• D

• E

ASSUME THE GIVEN DISTRIBUTION IS NORMAL.

• A

• B

• C

• D

• E

Which of the following distributions will best be modeled by a normal distribution?

• A bimodal distribution with a peak at 3, a peak at 10, and a standard deviation of 5.

• A uniform distribution with a mean of 5 for which 20% of the observations are between 1 and 3.

• A binomial distribution with n=150 and p=0.5.

• A geometric distribution with p=0.9

• A chi-square distribution with 2 degrees of freedom.

Answer explanation

The correct answer is (C). A binomial distribution with n = 150 and p = 0.5 can be modeled by a normal distribution because np = 150(0.5) = 75 ≥ 10 and n(1 – p) = 150(0.5) ≥ 10. 

Have you ever run into someone you know when you were far away from home? A random sample of 1000 adults were asked this question. Here are their responses: Based on the responses, which of the following is a 90 percent confidence interval for the proportion of all adults who would respond that they have run into someone they know when they were far away from home?

• 0.801 ± 0.0325

Answer explanation

There are forty multiple-choice questions on this exam, each having answer choices A, B, C, D, or E. Only one answer choice per question is correct. Suppose a student randomly guesses their answer choice to each question, and their guesses from question to question are independent. Which of the following is the probability that the student guesses at least 12 questions correctly on this portion of the exam?

• 0.0238

• 0.0442

• 0.0875

• 0.9125

• 0.9806

Answer explanation

A machine at a manufacturing company is programmed to fill shampoo bottles such that the amount of shampoo in each bottle is normally distributed with mean 0.60 liter and standard deviation 0.04 liter. Let the random variable A represent the amount of shampoo, in liters, that is inserted into a bottle by the filling machine. A bottle is considered underfilled if it has less than 0.50 liter of shampoo. Determine the probability that a randomly selected bottle of shampoo will be underfilled. 

• .9938

• .0062

• -2.5

• none of these

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

There are 20 multiple-choice questions on an exam, each having four possible responses, of which only one is correct. Each question is worth 5 points if answered correctly. Suppose that a student guesses the answer to each question, with her guesses from question to question being independent. The standard deviation of the student's score on the exam is

• 1.94

• 4.33

• 9.68

• 21.65