probability

Question

A basketball player makes a successful free throw 86% of the time. Using the Normal approximation to the binomial, estimate the probability that he makes between 30 and 40 successful shots in 50 free throw attempts (including 30 and 40)

Answer 1

For a normal approximation, find the average: np=.86*50=34.

Then find the standard deviation: sqrt(np(1-p))=sqrt(50*.86*.14)=2.4

 

Then the resulting number of standard deviations for 30 and 40 successful shots out of fifty:

30 shots: (30-34)/2.4=-1.67

40 shots: (40-34)/2.4=4.167

 

Then find the resulting probabilities of each end of the range using Excel

normsdist(-1.67)=.04746

normsdist(4.167)=.9999

 

Then P(30<=X<=40)=P(X<40)-P(X<30)=.9999-.04746=.9525

 

Hope that helps,

Deanna