Question

A toolbox contains 71 nails, of which 34 nails are 4 inches long and 37 are 8 inches long. If a sample of 27 nails is randomly selected from the toolbox.

(i) What is the probability that there are at least 2 four-inch-long nails in the sample?

(ii) What is the standard deviation of the number of 8-inch-long nails in the sample?

Answer 1

a)Let X4 = no. of four-inch-long nails; then p=34/71 and q=37/71, n=27

P(X4>=2) = 1- P(X4=0) - P(X4=1)

P(X4=0) = 27C0*(34/71)^0*(37/71)^27

=(37/71)^27

P(X4=1) = 27C1*(34/71)^1*(37/71)^26

=(27*34*(37/71)^26)/71

P(X4>=2) = 1- P(X4=0) - P(X4=1)

b)Let X8 = no. of eight-inch-long nails; then p=37/71 and q=34/71, n=27

Variance = npq = 27*37/71*34/71 = 6.7379

SD = sqrt(var) = 2.5958