Question

In 1999, 2.2% of all cars in the United States were reported stolen. In a random sample of 400 Nissan Maxima cars 12 were reported stolen during 1999. If the percentage of thefts for Nissan Maxima cars is the same as the national percentage of 2.2%, what is the probability that the percentage of thefts ina random sample of 400 would be greater than or equal to 3%

Answer 1

The probability of the percentage of thefts in a random sample of 400 would be greater than or equal to 3 is given by P (z> 1.09) = 0.1379

Explanation:

The statistic

z= p^- p / √pq/n

is used to measure the difference between the sample and population proportions.

Here p^= 12/400= 0.03

p= 0.022 q= 1-0.022=0.978

and n=400

Putting the values

Z= 0.03-0.022/√0.022(1-0.022)/400

Z= 0.008/√0.022(0.978)/400

Z= 0.008/0.00733

z= 1.090

We have to find the probability of the percentage of thefts in a random sample of 400 would be greater than or equal to 3

or

Mathematically

P (z> 1.09)= 1- P (z≤1.09)

= 1- 0.8621 ( from the z area table)

= 0.1379