Of those mountain climbers who attempt Mt. McKinely (Denali), only 65% reach the

Question

Of those mountain climbers who attempt Mt. McKinely (Denali), only 65% reach the summit. In a random sample of 16 mountain climbers who are going to attempt Mt.McKinely, what is the probability of each of the following
A) all 16 reach the summit
B) at least 10 reach the summit
C) No more than 12 reach the summit.
D) from 9 to 12 reach the summit, including 9 and 12. Of those mountain climbers who attempt Mt. McKinely (Denali), only 65% reach the summit. In a random sample of 16 mountain climbers who are going to attempt Mt.McKinely, what is the probability of each of the following
A) all 16 reach the summit
B) at least 10 reach the summit
C) No more than 12 reach the summit.
D) from 9 to 12 reach the summit, including 9 and 12.
A) all 16 reach the summit
B) at least 10 reach the summit
C) No more than 12 reach the summit.
D) from 9 to 12 reach the summit, including 9 and 12.

Explanation / Answer

Ans:

Binomial distribution with n=16,p=0.65

P(x=r)=16Cr*0.65r*(1-0.65)16-r

a)P(x=16)=16C16*0.6516*0.350=0.6516=0.0010

b)P(x>=10)=1-P(x<=9)=1-BINOMDIST(9,16,0.65,TRUE)=1-0.3119=0.6881

c)P(x<=12)=BINOMDIST(12,16,0.65,TRUE)=0.8661

d)P(9<=x<=12)=P(x<=12)-P(x<=8)

=BINOMDIST(12,16,0.65,TRUE)-BINOMDIST(8,16,0.65,TRUE)

=0.8661-0.1594

=0.7067

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