Question

At a large business, employees must report to work at 7:30 A.M. The arrival times of employees is approximately symmetric and mound-shaped with mean 7:22 A.M. and standard deviation 4 minutes.
Question 1. Use the 68-95-99.7 rule (also known as the Empirical rule) to determine what percent of employees are late on a typical day.

Question 2. A psychological study determined that the typical worker needs four minutes to adjust to their surroundings before beginning their duties. Use the 68-95-99.7 rule (also known as the Empirical rule) to determine what percent of this business? employees arrive early enough to make this adjustment before the 7:30 A.M. start time.

Answer 1

Answer:

(a) 2.5%

(b) 84%

Step-by-step explanation:

Applying the empirical rule,

68% arrive within 7:22 am +/- 4 minutes (7:18 am to 7:26 am)

95% arrive within 7:22 am +/- 8 minutes (7:14 am to 7:30 am)

99.7% arrive within 7:22 am +/- 12 minutes (7:10 am to 7:34 am)

(a) Those that arrive late arrive after 7:30 am. Half of all employees (50%) arrive after 7:22 am.

Since the arrival time is symmetric, half of those that arrive between 7:14 am and 7:30 am (95%) arrive between 7:22 am and 7:30 am.

This means 95% ÷ 2 = 47.5% arrive before 7:30 am.

The late arrivals = 50% - 47.5% = 2.5%

(b) Those who come early to make the adjustment come 4 minutes before 7:30 am = 7:26 am.

50% come before 7:22 am.

Since the arrival time is symmetric, half of those that arrive between 7:18 am and 7:26 am (68%) arrive between 7:22 am and 7:26 am. This means 68% ÷ 2 = 34% arrive between 7:22 am and 7:26 am.

The percentage that arrive before 7:26 am = 50% + 34% = 84%.