Question

Suppose the amount of tar in cigarettes is normally distributed with mean 3.5 mg and standard deviation 0.5 mg.

a.) What proportion of cigarettes have a tar content exceeding 4.25 mg?

b.) "Low tar" cigarettes must have tar content below the 25^th percentile of the tar content distribution. What is the value, which is the 25^th percentile of the tar content distribution?

Answer 1

Suppose, random variable X denotes amount of tar (in mg) in cigarettes.

From the given data,

(a)

Required proportion (probability) is given by

   [Using R-code 'pnorm(1.5)']

Hence, proportion of cigarettes in which tar content exceeds 4.25 mg is 0.0668072.

(b)

Using R-code 'qnorm(0.25)' we have,

Hence, 3.162755 mg is the 25 th percentile of the tar content distribution.