SOLUTION: Given a binomial distribution where n=50 and p=0.17. Which of the following is considered an unusual event? a) P(x=8.5) b) P(x=12) c) P(x=15) d) P(x=6)

 

Hi,

Given a binomial distribution where n=50 and p=0.17

mean =  = 8.5

SD = sqrt(50*.17*.83) = 2.66

Note: We can use the normal distribution as a close approximation to the

 binomial distribution whenever np ≥ 5 and nq ≥ 5.

Note: np = 8.5  and nq = 41.5

Which of the following is considered an unusual event?

Using a normal distribution as a close approximation to this binomial distribution

 a) P(x=8.5) mean 

 b) P(x=12) close to 1 SD from mean ( 8.5 + 2.66 = 11.16)

 c) P(x=15) unusual event (beyond 2 SDs from mean)

 d) P(x=6)  close to 1 SD from mean (8.5-2.66 = 5.84  )