Question

In a certain population of the eastern thwump bird, the wingspan of the individual birds follows an approximate normal distribution with mean 53.0mm and a standard deviation 6.25mm. A sample of five birds is drawn from the population.

(A) Find the probability that the wingspan of the first bird chosen is between 48mm and 58mm long?
(B) Find the probability that at least one of the five birds has a wingspan between 48mm and 58mm long?
(C) What is the expected number of birds in this sample whose wingspan is between 48mm and 58mm long?

Answer 1

Explanation:

given that in a certain population of the eastern thwump bird, the wingspan of the individual birds follows an approximate normal distribution with mean 53.0mm and a standard deviation 6.25mm.

a) P(48<x<58) where X is N(55,6.25)

=0.7881- 0.2119

=0.5762

b) Now each bird is independent of the other and hence Y no of birds between 48 and 58 is binomial with n =5 and p = 0.5762

Prob atleast one bird =
`P(X\geq 1)\\=1-P(0)\\= 1-(1-0.5762)^5\\=0.9365`

c) Expected no = np

= 0.881