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Applied Math 40S Slides April 2, 2007

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More about binomial distributions and normal approximations of binomial distributions. Also, an introduction to 95% confidence intervals.

More about binomial distributions and normal approximations of binomial distributions. Also, an introduction to 95% confidence intervals.

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  • 1. The probability that a student owns a CD player is 3/5. If eight students are selected at random, what is the probability that: (a) exactly four of them own a CD player? (b) all of them own a CD player? (c) none of them own a CD player?
  • 2. A basketball player is successful on her free throws 75% of the time. Determine the probability that she makes at least 7 out of her next 10 free throws by: Calculating the probability as a binomial distribution. [binompdf(# trials, Probability of success)] Calculating the probability using a normal approximation of the binomial distribution. What is the difference between these two answers?
  • 3. A basketball player is successful on her free throws 75% of the time. Determine the probability that she makes at least 7 out of her next 10 free throws by: Calculating the probability using a normal approximation of the binomial distribution.
  • 4. A basketball player is successful on her free throws 75% of the time. Determine the probability that she makes at least 21 out of her next 30 free throws by: Calculating the probability as a binomial distribution. [binompdf(# trials, Probability of success)] Calculating the probability using a normal approximation of the binomial distribution. What is the difference between these two answers?
  • 5. A basketball player is successful on her free throws 75% of the time. Determine the probability that she makes at least 21 out of her next 30 free throws by: Calculating the probability using a normal approximation of the binomial distribution. What is the difference between these two answers?
  • 6. A basketball player is successful on her free throws 75% of the time. Determine the probability that she makes at least 42 out of her next 60 free throws by: Calculating the probability as a binomial distribution. [binompdf(# trials, Probability of success)] Calculating the probability using a normal approximation of the binomial distribution. What is the difference between these two answers?
  • 7. A basketball player is successful on her free throws 75% of the time. Determine the probability that she makes at least 42 out of her next 60 free throws by: Calculating the probability using a normal approximation of the binomial distribution.
  • 8. Summary for scoring on 70% of all shots taken... # of trials Binomial Probability Probility using Normal Approximation 10 30 60 Examine the results in the table. Do you notice any pattern?
  • 9. In a normal distribution, what percent of all the data lie within 2 standard deviations of the mean?
  • 10. Between what two z-scores will you find exactly 95% of all data in a standard normal distribution?
  • 11. The student council is planning a spring dance. They need to sell 85 tickets in order to cover their costs. Records show that, on average, 10% of the students enrolled at the school attend dances. This year there are 1052 students enrolled at the school. Construct a 95% confidence interval for the number of students who will attend the spring dance. Will the student council sell enough tickets to cover their costs? Yup. With a more than 95% probability.