Question

Police estimate that 89% of drivers now wear their seat belts. They set up a safety roadblock, stopping 140 cars to check for seat belt use.a) Find the mean and standard deviation of the number of drivers expected to be wearing seat belts.b) What's the probability they find at least 27 drivers not wearing their seat belts?a) The mean is and the standard deviation is(Type integers or decimals rounded to two decimal places as needed.)b) The probability is(Type integers or decimals rounded to four decimal places as needed.)

Answer 1

Given data:

a)

The expression for the mean number of drivers expected to be wearing seat belts is,

`\begin{gathered} m=(89)/(100)*140 \\ =124.6 \\ \approx125 \end{gathered}`

The expression for the standard deviation of drivers expected to be wearing seat belts is,

`\begin{gathered} s=\sqrt[]{(0.89)(1-0.89)*140} \\ =\sqrt[]{13.706} \\ =3.702 \end{gathered}`

Thus, the mean number of drivers expected to be wearing seat belts is 125, and the standard deviation of drivers expected to be wearing seat belts is 3.702.