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%.