In a large business statistics class the professor has each

In a large business statistics class, the professor has each person select stocks by throwing 16 darts at pages of a business newspaper. They then check to see whether their stock picks rose or fell the next day and report their proportion of \"successes.\" As a lesson the professor has selected pages of the newspaper for which exactly half the publicly traded stocks went up and half went down. The professor then makes a histogram of the reported proportions. Complete parts a through d below. a) What shape would you expect this histogram to be? Why? Skewed left because probabilities of success and failure are not equal Skewed right because probabilities of success and failure are not equal Skewed left because probabilities of success and failure are equal Symmetric, because probabilities of success and failure are not equal Symmetric, because probabilities of success and failure are equal Skewed right because probabilities of success and failure are equal

Solution

Answer: E

Half of the stocks went up and half went down.

The proportion of stocks that went up =1/2

Now, every student selects 16 stocks (or 16 trials using a dart) where each trial is Bernoulli(0.5)

So, each student encounters number of successes distributed as Binomial (16, 0.5)

That means the number of success for each student is an observation from Binomial (16, 0.5) independent of the other.

So, the (frequency of) proportion of success (number of success/16) plotted for a very large number of students will resemble that of a Binomial(16, 0.5) distribution.

Since, success probability for this distribution, p=0.5, the plot will be symmetrical.