Question

For a binomial probability distribution, it is unusual for the number of successes to be less than μ − 2.5σ or greater than μ + 2.5σ. (a) For a binomial experiment with 10 trials for which the probability of success on a single trial is 0.2, is it unusual to have more than five successes? a. Yes. The upper limit of successes that would be deemed to be usual is 5, so more than 5 successes would be unusual. b. Yes. The upper limit of successes that would be deemed to be usual is 6, so more than 5 successes would be unusual. c. No. The upper limit of successes that would be deemed to be usual is 5, so more than 5 successes would not be unusual. d. No. The upper limit of successes that would be deemed to be usual is 6, so more than 5 successes would not be unusual.

Answer 1

Answer:The correct option is a)

The upper limit of successes that would be deemed to be usual is 5, so more than 5 successes would be unusual.

Explanation:

The mean of a binomial distribution

μ= np where n=10 and p= 0.2 q= 1-p, q= 1-0.2=0.8

μ= 10×0.2=2

σ=√npq

σ=√10×0.2×0.8=1.26

Is unusual for the number of success to be greater than μ + 2.5σ.

= 2+2.5(1.26)

=5 approximately.

So it is unusual for it to be greater than 0.5. The right option Is a)