Question

# A study by Allstate Insurance Co. finds that 82% of teenagers have used cell phones while...

A study by Allstate Insurance Co. finds that 82% of teenagers have used cell phones while driving. Suppose a random sample of 100 teen drivers is taken.

What is the standard deviation of proportion of 100 teen drivers who use cell phone while driving? Please provide an answer with 3 decimal points.

Let X be the number of teenagers who uses cell phone while driving.

Then X follows binomial probability with

p = success probability = 0.82,

q = failure probability = 1 - p = 0.18

n = number of trials (teen drivers) = 100,

Since sample size (n) is large enough, so as per central limit theorem, the distribution of sample mean will follow normal distribution with mean and standard deviation as defined below

Mean = n*p

And standard deviation = sqrt (n*p*q) where q = 1 - p = 1 - 0.82 = 0.18

So, standard deviation of proportion of 100 teen drivers who use cell phone while driving = sqrt (npq)

= sqrt (100*0.82*0.18) = sqrt (14.76) = 3.8419 = 3.842 (answer)