You randomly select 100 drivers ages 15 to 19 from Example 4. What is the probability that the mean time they spend driving each day is between 24.7 and 25.5 minutes? Use μ = 25 minutes and σ = 1.5 minutes.

a. Use the Central Limit Theorem to find μ_x̅ and σ_x̅ and sketch the sampling distribution of the sample means.

b. Find the z-scores that correspond to x̅ = 24.7 minutes and x̅ = 25.5 minutes.

c. Find the cumulative area that corresponds to each z-score and calculate the probability that the mean time spent driving is between 24.7 and 25.5 minutes.

d. Interpret the results.

Example 4

Time behind the wheel The average time spent driving each day, by age group: 15-19 25 minutes 20-24 52 25-54 64 55-64 58 65+ 39