In: Statistics and Probability
It is known that 76.3% of all high school students age 16 or older in the United States have driven a car in the past month. Suppose you take a random sample of 82 high school students age 16 or older. What is the probability that less than 70% of the students in your sample have driven a car in the past month?
a) 0.0901
b) 0.1075
c) 0.2776
d) this cannot be determined as the central limit theorem conditions are violated.
Solution:
Given that,
n = 82
= 0.763
1 -
= 1 - 0.763 = 0.237
So,
=
= 0.763
=
( 1 -
) / n
=
0.763 * 0.237 / 82
= 0.0470
= 0.0470
p (
< 0.70 )
p (
-
/
) < ( 0.70 - 0.763 / 0.0470 )
p ( z < -0.063 / 0.0470 )
Using z table
p ( z < -1.34 )
= 0.0901
Probability = 0.0901
Option A ) is correct.