Question

it is estimated that 30% of households own a riding lawn mower. a sample of 16 households is studided, what is the standard deviation of the nunber of households who own a riding lawnmower?

4.8

16

1.833

3.36

Answer 1

it is estimated that 30% of households own a riding lawn mower. a sample of 16 households is studied, what is the standard deviation of the nunber of households who own a riding lawnmower?

Here the household can own a riding lawn mover or can not hold a riding lawn mover. There are only two possibilities or outcomes possible. So this is a binomial distirbution

Varaince of a binomial distribution = n * p * (1 - p)

Here n = 16 which is number of households in the sample that are studied

p = 0.3 since 30% of households own a riding lawn mower

So Vairance = 16 * 0.3 * (1 - 0.3)

= 16 * 0.3 * 0.7

= 3.36

We know that Standard deviation = Variance

So Standard deviation here = 3.36

= 1.833

So Answer is Option C