Question

According to a local insurance company, 23% of drivers aged 60 - 62 fail the written driver's test. With the conditions of the Binomial distribution being satisfied if we had randomly picked 10 of the drivers from this age group, then find the following:

a) The probability that exactly 3 of the 10 drivers aged 60 - 62 fail the written driver's test. Round answer to 3 decimal places.

b) The mean and the standard deviation of this Binomial distribution. Round the standard deviation to 3 decimal places.

Answer 1

a) we have n = sample size = 10

p = proportion of drivers aged 60-62 faile the written drivers test = 0.23

We asked P( X = 3)

Using binomial probability

P( X = 3) = 10!/3!*7! *(0.23)3*(0.77)7

P( X = 3) = 0.234

b) mean = n * p = 10* 0.23

Mean = 2.300

Standard deviation   = sqrt [ n *p*q] = sqrt [10*0.23"0.77]

Standard deviation = 1.331