A basketball player shoots 60 free throws a day and historically makes 75 percent of them.What is the probability that he will make at most 80 percent tomorrow?
A)0.1056
B)0.8133
C)0.1867
D)0.8944

Question

Quizplus · Accepted Answer

The probability of making at most 80% of the free throws can be calculated using the binomial distribution or approximated using the normal distribution since the sample size is large (n=60). Historically, the player makes 75% of the shots, so the expected number of shots made is 45 (75% of 60). To find the probability of making at most 48 shots (80% of 60), we can use the normal approximation to the binomial distribution. The standard deviation σ for the binomial distribution is sqrt(n*p*(1-p)) = sqrt(60*0.75*0.25) = sqrt(11.25) ≈ 3.35. Using the normal approximation, we find the z-score for 48 shots made, adjust for continuity by subtracting 0.5 from 48, resulting in a z-score less than or equal to (47.5-45)/3.35. Looking up this z-score in a standard normal distribution table or using a calculator gives a probability of approximately 0.8133, indicating the likelihood of making at most 48 (or 80%) of the shots is about 81.33%.

A Basketball Player Shoots 60 Free Throws a Day and Historically