Question

Jack correctly guesses the answer to a question 74% of the time. If he guess for all 7 questions assuming that each question is independent of the next. What are the standard deviation for the number of questions he would correctly guess?

Answer 1

Answer: Let's first find the expected value or the mean number of questions Jack would correctly guess:

Expected value = mean = n * p = 7 * 0.74 = 5.18

where n is the number of trials (7) and p is the probability of success (0.74).

The variance of the number of correct guesses is given by:

Variance = n * p * (1 - p) = 7 * 0.74 * (1 - 0.74) = 1.7

The standard deviation is the square root of the variance:

Standard deviation = sqrt(Variance) = sqrt(1.7) ≈ 1.30

Therefore, the standard deviation for the number of questions Jack would correctly guess is approximately 1.30.

Explanation: