Out of a sample of 50 golfers, 13 can shoot below 90. The other 37 cannot. You r

Question

Out of a sample of 50 golfers, 13 can shoot below 90. The other 37 cannot. You randomly choose 3 golfers. a) What is the probability all 3 can shoot below 90? b) What is the probability none of them can shoot below 90? c) What is the probability exactly one can shoot below 90? d) What is the probability at least one can shoot below 90? 58% of golfers use Titleist golf balls. Find the probability if 500 golfers are selected more than 260 of them use Titleist. Use normal approximation to the binomial distribution.

Explanation / Answer

Question-2

Let X denote the number who shoot below 90. Then X follows Binomial distribution with n=3 and p=13/50=0.26

Part-a

P(all 3 can shoot below 90)=P(X=3)= 0.0176 using excel function =BINOMDIST(3,3,0.26,FALSE)

Part-b

P(no one shoot below 90)=P(X=0)= 0.4052 using excel function =BINOMDIST(0,3,0.26,FALSE)

Part-c

P(exactly on can shoot below 90)=P(X=1)= 0.4271 using excel function =BINOMDIST(1,3,0.26,FALSE)

Part-d

P(at least one can shoot below 90)=P(X>=1)=1-P(X=0)=1-0.4052=0.5948

Question-3

Let X denote the number who use Titleist golf balls. Then X follows Binomial distribution with n=500 and p=0.58

As n is large , so X follows normal distribution with mean=np=500*0.58 =290 and standard deviation =sqrt(np(1-p)=sqrt(500*0.58*(1-0.58))=11.04

So, P(more than 260 use Titleist)=P(X>260)

=0.9967 using excel function =1-NORMDIST(260,290,11.04,TRUE)

Related Questions

Navigate

• Browse (All)
• Browse O
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.