Question

A. A marine biologist has noticed unusually thin shells in some of the oysters found in a bay known for its oysters.   He thinks the thin shells are appearing in 10% of the oyster population in the bay. The marine biologist randomly selects 150 oysters from the bay and tests the oysters for the thin shell.

1. Is this study a Binomial model? Explain. (6 points)

2. What are the mean and the standard deviation of the random variable? (4 points)

3. Is it appropriate to use the normal approximation to the binomial for this problem? Support your answer with numbers and a test. (4 points)

Answer 1

(1)

This study is a Binomial model because it satisfies the following conditions:

(i) The total number of observations =n = 150 is fixed

(ii) Each observation is independent.

(iii) Each observation represents one of two outcomes

(iv) Probability of success = p = 0.10 is the same for each outcome.

(2)

(i) mean = np = 150 X 0.10 = 15

(ii) Standard deviation =

угру-V 150 0.10 0.90 3.6742

(3)

Normal approximation to the binomial for this problem is appropriate because it satisfies the following conditions:

(i) np = 150 X 0.10 = 15 > 5

(ii) n(1-p) = 150 X 0.90 = 135 > 5