AP Statistics Random Variable

In which of the following situations would it be appropriate to use a Normal distribution to approximate probabilities for a binomial distribution with the given values of n and p?

• n = 10, p = 0.5

• n = 40, p = 0.88

• n = 100, p = 0.2

• n = 100, p = 0.99

• n = 1000, p = 0.003

The weight of tomatoes chosen at random from a bin at the farmer’s market follows a Normal distribution with mean = 10 ounces and standard deviation  = 1 ounce. Suppose we pick four tomatoes at random from the bin and find their total weight T. The random variable T is

• Normal, with mean 10 ounces and standard deviation 1 ounce.

• Normal, with mean 40 ounces and standard deviation 2 ounces

• Normal, with mean 40 ounces and standard deviation 4 ounces

• binomial, with mean 40 ounces and standard deviation 2 ounces

• binomial, with mean 40 ounces and standard deviation 4 ounces.

A class of 20 students includes 14 seniors and 6 juniors. Each day, the teacher randomly selects an SRS of 4 students to present the answer to a homework question. Which of the following correctly describes one trial of a simulation to estimate the probability that all four chosen are juniors?

• Let 1 - 70 = senior and 71 - 100 = junior. Generate 4 random integers with replacement from 1 to 100 and count how many integers are between 71 and 100.

• Let 1 - 70 = senior and 71 - 100 = junior. Generate 4 random integers without replacement from 1 to 100 and count how many integers are between 71 and 100.

• Let 1 - 14 = senior and 15 - 20 = junior. Generate 4 random integers with replacement from 1 to 20 and count how many integers are between 15 and 20.

• Let 1 - 14 = senior and 15 - 20 = junior. Generate 4 random integers without replacement from 1 to 20 and count how many integers are between 15 and 20.

• Let 1 - 14 = senior and 15 - 20 = junior. Generate 6 random integers with replacement from 1 to 20 and count how many integers are between 15 and 20.

The weights of chocolate truffles made by a candy shop are approximately normally distributed with a mean of 2 ounces and a standard deviation of 0.3 ounce. a) What is the probability that a randomly selected chocolate truffle from this candy shop will weigh less than 1.5 ounces? b) The candy shop assembles gift boxes that contain 8 randomly selected chocolate truffles. What is the probability that none of the truffles in a gift box weighs less than 1.5 ounces? c) The weights of gift boxes, including all packaging materials, are approximately normally distributed with a mean of 3 ounces and a standard deviation of 0.5 ounce. If 8 randomly selected chocolate truffles are placed into a randomly selected gift box, describe the distribution of the total weight of the gift box and truffles.

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The distribution of commute times for the employees at a large company is skewed to the right with a mean of 22 minutes and a standard deviation of 14 minutes. If a human resources director selects a random sample of 50 employees, which of the following is closest to the probability that the sample mean commute time is less than 20 minutes?

A distribution of exam scores has a mean of 60 and a standard deviation of 18. If each score is doubled, and then 5 is subtracted from the result, what will the mean and standard deviation of new scores be?

• mean = 115
  standard deviation = 31

• mean = 115
  standard deviation = 36

• mean = 120
  standard deviation = 6

• mean = 120
  standard deviation = 31

• mean = 120
  standard deviation = 36

Suppose the population proportion of people who use public transportation to get to work in Washington, D.C., area is 0.45. In a simple random sample of 250 people who work in the city, about how far do you expect the sample proportion to be from the population proportion?

• 0.0010

• 0.0285

• 0.0315

• 0.4975

• 7.8661

What is the word in statistics for any characteristic or attribute of a person, place, or thing?

• variable

• descriptive statistic

• inferential statistic

• parameter

What is a quantitative variable that could have an infinite number of values?

• categorical variable

• qualitative variable

• discrete variable

• continuous variable

What is the branch of mathematics dealing with the collection, organization, analysis, interpretation and presentation of data?

• Algebra

• Geometry

• Probability

• Statistics