Question

1. A soccer team estimates that they will score on 66​% of the corner kicks. If this team has 197

corner kicks over the​ season, what are the chances that they score more than 22 ​times?

2. A basketball player has made 79​% of his foul shots during the season. Assuming the shots are​ independent, what's the expected number of shots until he​ misses?

Answer 1

1)

n=

197

p=

0.6600

here mean of distribution=μ=np=		130.02
and standard deviation σ=sqrt(np(1-p))=		6.65
for normal distribution z score =(X-μ)/σx

therefore from normal approximation of binomial distribution and continuity correction:

chances that they score more than 22 ​times:

probability =P(X>22.5)=P(Z>(22.5-130.02)/6.649)=P(Z>-16.17)=1-P(Z<-16.17)=1-0=1.0000 (almost certain)

2)

this is Geometric distribution with parameter p=1-0.79 =0.21

  expected number of shots until he​ misses=1/p =4.7619