Question

1. A survey from Veterinary Research Unlimited found that 80% of dogs do not have chronic ear infections. If 8 dogs are selected at random, find the probability that:

1. What is the mean and standard deviation of this distribution?

b. exactly 3 will not have chronic ear infections.

c. The value in part a should be quite small. Explain why this is the case using the words mean and standard deviation.

d. at least two of them will not have chronic ear infections.

Please show all work or if you used a TI-84 please explain any steps or functions you used to derive at the answer, thank you for the help :)

Answer 1

Let X = No. of dogs who do not have chronic ear infection.

n = 8 and p = 0.8

X follows Binomial distribution with parameter n and p.

The pmf of X is,

a.

Mean = np = 8 * 0.8 = 6.4

Standard deviation =

b.

c.

The value in part b should be quite small, Because its mean is 6.4 and standard deviation is 1.1314.

The value 3 is 3 standard deviation below the mean.

Mean - 3SD = 6.4 - 3 (1.1314)= 3.0038

According to empirical rule probability beyond 3 sigma limit is very low.

d.

P(at least two of them will not have chronic ear infections ) =