Summary: The Practice Of Statistics 7E

Read the summary and the most important questions on The Practice Of Statistics 7E

• 1 The Practice Of Statistics 7E

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• What is the AP® Exam Tip regarding Daily Videos?

  Review the content of this section and get extra help by watching the AP® Daily Videos for Topics 4.10–4.12, which are available in AP® Classroom.

• Why is \( X \) a binomial random variable in the spinner example?

  • \( X \) is a binomial random variable because:
    • There are a fixed number of trials (12 spins).
    • Each trial has two possible outcomes (blue or not blue).
    • The probability of landing in the blue region is constant (0.80).
    • Trials are independent.

• What are the steps for calculating probabilities involving binomial or geometric random variables?

  • Step 1: Define the random variable of interest, state how it is distributed, and identify the values of interest.
  • Step 2: Perform calculations—show your work.

• What is the probability that exactly 8 spins land in the blue region?

  • The probability that exactly 8 spins land in the blue region is calculated using the binomial probability formula with \( n = 12 \), \( p = 0.80 \), and \( X = 8 \).

• What is the mean and standard deviation of a geometric random variable X?

  The mean is \( \muX = \frac{1}{p} \) and the standard deviation is \( \sigmaX = \frac{\sqrt{1-p}}{p} \).

• Why is \( Y \) a binomial random variable in the red light example?

  • \( Y \) is a binomial random variable because:
    • There are a fixed number of trials (10 days).
    • Each trial has two possible outcomes (red or not red).
    • The probability of the light being red is constant (0.55).
    • Trials are independent.

• What is the probability that the light is red on exactly 7 days?

  • The probability that the light is red on exactly 7 days is calculated using the binomial probability formula with \( n = 10 \), \( p = 0.55 \), and \( Y = 7 \).

• What is Exercise 1 about in Section 4F?

  Exercise 1 involves determining whether a randomly selected baby elk with a 44% chance of surviving to adulthood is a binomial random variable and stating its probability distribution.

• What probability distribution does \( R \) have in the bag check example?

  • \( R \) has a binomial probability distribution because:
    • There are a fixed number of trials (20 passengers).
    • Each trial has two possible outcomes (red light or not).
    • The probability of a red light is constant (0.30).
    • Trials are independent.

• What does Exercise 4 in Section 4F involve?

  Exercise 4 involves determining if the number of days a train arrives on time, with a 90% chance, is a binomial random variable and stating its probability distribution.