A newspaper survey found that 65% of readers found online tutorials useful. If a random sample of 9 readers is selected, compute the standard deviation of the probability distribution.

Suppose you are given data from a survey showing the IQ of each person interviewed and the IQ of his or her mother. That is all the information you have. Your boss has asked you to put together a report showing the relationship between these two variables. What could you present and why?

To compute the standard deviation of the probability distribution for this problem, we need to determine the standard deviation of a binomial distribution.

A binomial distribution is used when there are two possible outcomes, success or failure, and each trial is independent and has the same probability of success.

In this case, the probability of "finding online tutorials useful" is considered a success, and the probability of "not finding online tutorials useful" is considered a failure. The given newspaper survey found that 65% of readers found online tutorials useful. Therefore, the probability of success is 0.65, and the probability of failure is 0.35 (1 - 0.65).

The formula for the standard deviation of a binomial distribution is:

σ = √(n * p * q)

Where:
σ = standard deviation
n = sample size
p = probability of success
q = probability of failure (1 - p)

In this case, the sample size (n) is 9, the probability of success (p) is 0.65, and the probability of failure (q) is 0.35.

Let's calculate the standard deviation:

σ = √(9 * 0.65 * 0.35)
= √(2.81775)
≈ 1.68

Therefore, the standard deviation of the probability distribution for this problem is approximately 1.68.