A study found that 82% of teenagers use cell phones while driving. If a random sample of 100 teen drivers is taken, the standard error for the sampling distribution of the sample proportion is 0.0488. The sampling distribution will be approximately normal. There is a 0.1587 probability that the sample proportion is less than 0.80. There is a 0.9500 probability that the sample proportion is within 0.02 of the population proportion of 0.82.

1. A study by Allstate insurance Co, finds that 82% of teenagers have used cell phones while
driving (The Wall Street Journal, May 5 . 2010). Suppose a random sample of 100 teen drivers is
taken. [You moy 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.) 0.2. Is the sampling distribution of the sample proportion
approximately normal? Yes No b. What is the probability that the sample proportion is less than
0.80 ? (Round " " vvalueto2 decimal ploces, and final answer to 4 decimal places.)
c. What is the probability that the sample proportion is within pm 0.02 of the population
proportion? (Round "z" value to 2 decime places, ond final answer to 4 decimal places.)