![A study by Allstate Insurance Co. finds that 82% of teenagers have used cell phones while driving (The Wal/Street Journal, May 5, 2010, Suppose a random sample of 100 teen drivers is taken. [You may find it useful to reference the z table.] a-1. Calculate the standard error for the sampling distribution of the sample proportion. (Do not round intermediate calculations. Round your answer to 4 decimal places.) Standard error a-2. Is the sampling distribution of the sample proportion approximately normal? O Yes No b. What is the probability that the sample proportion is less than 0.80? (Round value to 2 decimal places, and final answer to 4 decimal places.) Probability](https://i.imgur.com/81SX7Mm.png)
Answers
Solution:
a-1: Calculate the standard error for the sampling distribution of the sample proportion.
Answer: The standard error is:
a-2: Is the sampling distribution of the sample proportion approximately normal?
Answer: Yes
b. What is the probability that the sample proportion is less than 0.80?
Answer: The probability that the sample proportion is less than 0.80 is:
Now using the standard normal table, we have:
Therefore, the probability that the sample proportion is less than 0.80 is 0.3015
c. What is the probability that the sample proportion is within of the population proportion?
Answer:
Now using the standard normal table we have:
Therefore, the probability that the sample proportion is within of the population proportion is 0.3970
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