Question

Suppose the probability that a randomly selected PGA Tour player uses a Titleist brand golf ball is 0.65. For a sample of 9 PGA Tour players, find the probability that no less than 8 use a Titleist brand golf ball.

Answer 1

To determine the probability that at least 8 out of 9 PGA Tour players use a Titleist golf ball, we sum the binomial probabilities of exactly 8 players and all 9 players using Titleist using the binomial distribution formula or a calculator with statistical functions.

Step-by-step explanation:

To find the probability that no less than 8 PGA Tour players out of a sample of 9 use a Titleist brand golf ball, we can use the binomial probability formula. Given that the probability of a randomly selected PGA Tour player using a Titleist golf ball is 0.65, we can calculate the probabilities for exactly 8 players and all 9 players using Titleist. Since the question asks for 'no less than 8', we need to sum these two probabilities.

1. Calculate the probability of exactly 8 players using Titleist:
   P(X=8) = binompdf(9, 0.65, 8).
2. Calculate the probability of all 9 players using Titleist:
   P(X=9) = binompdf(9, 0.65, 9).
3. Sum the probabilities for 'no less than 8':
   Total Probability = P(X=8) + P(X=9).

Note that the actual calculation can be done using a calculator with statistical functions like the TI-83, 83+, 84, or 84+, using the binompdf function. This will give us the required probabilities directly.