Question

In: Statistics and Probability

It is known that 76.3% of all high school students age 16 or older in the...

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.

Expert Solution

Solution:

Given that,

n = 82

= 0.763

1 - = 1 - 0.763 = 0.237

So,

= = 0.763

= $\sqrt$ ( 1 - ) / n

= $\sqrt$ 0.763 * 0.237 / 82

= 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.

orchestra answered 2 years ago

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