Question

A bag contains 100 golf balls, 66 of which are red. Consider drawing a red golf ball to be a "success". If 31 golf balls are drawn with replacement, the result forms a binomial distribution.

a. What is the probability that the fifth draw will be a "success"?
b. What is the mean (
�
μ)?
c. What is the value of the standard deviation (
�
σ)?

Answer 1

a. The probability that the fifth draw will be a 'success' is calculated using the binomial probability formula. b. The mean of a binomial distribution is calculated using the formula μ = n * p. c. The standard deviation of a binomial distribution is calculated using the formula σ = √(n * p * (1 - p)).

Step-by-step explanation:

a. The probability that the fifth draw will be a 'success' can be calculated using the binomial probability formula: P(X = k) = (n Choose k) * p^k * (1 - p)^(n - k). In this case, n = 31, k = 5, and p = 66/100. Plugging in the values, we get P(X = 5) = (31 Choose 5) * (0.66)^5 * (0.34)^(31 - 5).

b. The mean (μ) of a binomial distribution can be calculated using the formula μ = n * p. In this case, n = 31 and p = 66/100. Substituting the values, we get μ = 31 * 0.66.

c. The standard deviation (σ) of a binomial distribution can be calculated using the formula σ = √(n * p * (1 - p)). In this case, n = 31 and p = 66/100. Plugging in the values, we get σ = √(31 * 0.66 * (1 - 0.66)).