Question

los angeles workers have an average commute of 29 minutes. suppose the la commute time is normally distributed with a standard deviation of 13 minutes. a. find the probability that a randomly selected la worker has a commute that is longer than 40 minutes. select b. if 3000 drivers are on the road, how many will have a commute less than 20 minutes? select

Explanation:

Step1: Calculate z-score for 40 mins

$z = \frac{X - \mu}{\sigma} = \frac{40 - 29}{13} = \frac{11}{13} \approx 0.85$

Step2: Find $P(Z > 0.85)$

$P(Z > 0.85) = 1 - P(Z \leq 0.85) = 1 - 0.8023 = 0.1977$

Step3: Calculate z-score for 20 mins

$z = \frac{20 - 29}{13} = \frac{-9}{13} \approx -0.69$

Step4: Find $P(Z < -0.69)$

$P(Z < -0.69) = 0.2451$

Step5: Calculate number of drivers

$\text{Number} = 3000 \times 0.2451 = 735.3 \approx 735$

Answer:

A. 0.198 (or ~0.20)
B. 735