Question

Suppose that 84% of the cases of car burglar alarms that go off are false. Let p be the proportion of false alarms in a random sample of 110 cases of car burglar alarms that go off. Calculate the mean and standard deviation of p and describe the shape of its sampling distribution.

Round your answer to four decimals places if necessary

up= ______
op= ______

The sampling distribution of p is normal or skewed to the right?

Answer 1

0.84 ; 0.0349545 ; symmetric

Explanation:

Given that:

p = proportion of false alarm

Sample size (n) = 110

The mean of p

Since 84% of car buglar alarms turns out as false, then, the mean value of p = 0.84

To obtain the standard deviation ; we use the relation ;

√(p(1 - p) / n)

Standard deviation :

√0.84(1 - 0.84) / 110

√0.84(0.16) / 110

√0.1344 / 110

√0.0012218

= 0.0349545

np = 110 * 0.84 = 92.4 (distribution is symmetric or normal)