2/27/2013

Wrap up normal probability plots and simulation results (See ProbPlot.MPJ)

Approximating Binomial Probabilities

• Graphical Display with Minitab (Graph > Probability Distribution Plot)

Normal Approximation for Counts

• Suppose that you flip a balanced coin 1000 times.  What is the probability of getting at most 532 heads?

Lab Exercises 

• Let the random variable X be the number of successes in n=30 independent Bernoulli trials with probability p=0.6 of success on each trial.  Find the probability of getting at most 25 successes in the n=30 independent trials.

a.  Use the binomial distribution.
b.  Use the normal approximation.

• Suppose that Kenyon College would like to have an entering class of 415 students next year.  Past experience shows that about 27% of the students admitted will accept  Kenyon's offer.  Answer the following questions assuming that the college decides to admit 1400 students and the students make their decisions independently.

a.  What is the distribution of the number of students who accept?
b.  What are the mean and variance of the number of students who accept?
c.  What is the probability that the college gets more students than they want?
d.  The college actually admitted 1535 students.  Redo part (c) using this information.

Normal Approximation for Proportions

Return to exercise on Binomial Lab. Use the sample proportion to approximate the probability of getting at most 25 heads in 30 flips of a biased coin with probability .6 of getting a head.

A corporation receives 100 applications for a position from recent college graduates in business. Assuming that these applications can be regarded as a random sample of all such graduates, what is the probability that between 25% and 35% of them are women if 30% of all recent college graduates in business are women?

Please read Sections 8.2 and 8.3 for class on Friday.