A survey from Veterinary Research Unlimited found that 80% of dogs do not have chronic ear...

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:

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

b. exactly 3 will not have chronic ear infections.

c. The value in part b 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.

e. Why is this value so high? Explain why this is the case using the words mean and standard deviation.

f. no more than 5 will not have chronic ear infections.

Solutions

Expert Solution

Answer a) Mean = 6.4 and Standard Deviation = 1.1314

Answer b) 0.0092

Answer c) 0.9999

Mean = 6.4

Standard Deviation = 1.1314

Mean - 2*Standard Deviation = 6.4 - 2*1.1314 = 4.1372

Since the value 3 is more than 2 standard deviation away from the mean, the value in part b should be quite small

Answer d)

We have to find P(X ≥ 2)

P(X ≥ 2) = 1 - P(X ≤ 1)

P(X ≥ 2) = 1 - P(X ≤ 1) = 1 - 0.0001

P(X ≥ 2) = 0.9999

Answer e) 0.2031

orchestra answered 1 year ago

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