Question

The length of one kind of fish is 3.5 inches, with a standard deviation of 0.2 inches. What is the probability that the average length of 100 randomly selected fishes is between 3.5 and 3.52 inches?

a) 0.9332

b) 0.4332

c) 0.8413

d) 0.3413

Answer 1

We do not the know the distribution of the length of fish. But we want to work with the average length of a sample. The sample size n = 100 > 30, so we can use the central limit theorem to find the distribution of average length.

CLT stats that if the sample size is large ( n > 30) then the distribution of the means of similar sample size will follow normal distribution.

= 3.5 = 0.2 n=100

then we use the normal probability tables to find the probabilities

P(3.5 < <3.52) = P( < 3.52) - P( < 3.5)

= P( Z < 1) - P(Z < 0)

= 0.8413- 0.5

Ans: 0.3413

d) 0.3413