What is the mean of this sampling distribution? What is the standard deviation for this sample? (Assume we are doing 100 SRSs)

Question

Mr. Haupt believes that it’s common knowledge that Skittles all have the same flavor. And that flavor is gross. Much to his surprise, he finds out that some of his students do not believe this well established opinion. After a preliminary experiment conducted by Emmie, we found that the odds of correctly distinguishing the color of the Skittles by a blind taste test is about 17%.

Answer 1

The mean of the sampling distribution is the same as the probability of correctly identifying a Skittle's color, which is 17%. So, the mean here is 0.17. To find the standard deviation (which tells us how much the results might vary), we use a formula that takes into account the probability and the sample size. Since the probability is 17% and we're using a sample size of 100, the standard deviation comes out to be about 0.038. This means that in different samples of 100 students, the proportion of correct guesses will usually vary by about 0.038 from the mean.

Here is the equation we use:

Standard Deviation = √p(1-p) / n, where p would be 0.17 and n would be the sample size of 100.

Standard Deviation = √0.17(1-0.17) / 100

= √0.17(0.83) / 100

= 0.038