Answers NC-Math 4 Calculating Probabilities for Sampling DistributionQuestion 6

6

QuizMultiple Choice

Calculating Probabilities for Sampling Distribution

Question 6 • NC-Math 4

In a large urban high school, 68% of the students take public transportation to and from school. Annette takes a random sample of 75 students from this school. What is the probability that more than 70% of the students in the sample take public transportation to and from school?Find the z-table here.

Answer

A

0.356

B

0.371

C

0.488

D

0.644

Explanation

The sample proportion has mean 0.68 and standard error √(0.68 × 0.32 ÷ 75) ≈ 0.054. For a sample proportion of 0.70, z = (0.70 − 0.68) ÷ 0.054 ≈ 0.37; the area to the right of z = 0.37 is about 0.356. Therefore, the probability is 0.356, choice A.

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