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Binomial Distributions, Geometric Distributions, and Sampling Distributions Rapid Review for AP Statistics

By — McGraw-Hill Professional
Updated on Feb 4, 2011

Review the following concepts if necessary:

Rapid Review

  1. A coin is known to be unbalanced in such a way that heads only comes up 0.4 of the time.
    1. What is the probability the first head appears on the 4th toss?
    2. How many tosses would it take, on average, to flip two heads?
  2. Answer:

    1. P(first head appears on fourth toss) = 0.4 (1 – 0.4)4–1 = 0.4(0.6)3 = 0.0864
    2. Average wait to flip two heads = 2(average wait to flip one head) = .
  3. The coin of problem #1 is flipped 50 times. Let X be the number of heads. What is
    1. the probability of exactly 20 heads?
    2. the probability of at least 20 heads?
  4. Answer:

    1. P(X =20) = [on the TI-83/84: binompdf(50, 0.4,20).]
    2. P(X ≥ 20) = = 1-binomcdf(50,0.4,19)=0.554.
  5. A binomial random variable X has B(300, 0.2). Describe the sampling distribution of .
  6. Answer: Since 300(0.2) = 60 ≥ 10 and 300(0.8) = 240 ≥ 10, has approximately a normal distribution with .

  7. A distribution is known to be highly skewed to the left with mean 25 and standard deviation 4. Samples of size 10 are drawn from this population and the mean of each sample is calculated. Describe the sampling distribution of .
  8. Answer: .

    Since the samples are small, the shape of the sampling distribution would probably show some left-skewness but would be more mound shaped than the original population.

  9. What is the probability that a sample of size 35 drawn from a population with mean 65 and standard deviation 6 will have a mean less than 64?
  10. Answer: The sample size is large enough that we can use large-sample procedures. Hence,

    .

    On the TI-83/84, the solution is given by normalcdf(-100,64, 65, ).

Review the following concepts if necessary:

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