Question

At a large business, employees must report to work at 6:30 A.M. The arrival times of employees is approximately symmetric and mound-shaped with mean 6:26 A.M. and standard deviation 2 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 2 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 6:30 A.M. start time.

%

Answer 1

According to the Empirical rule, 68%, 95% and 99.7% data lies within 1, 2 and 3 standard deviations of mean respectively

Mean = 6:26 AM

standard deviation is 2 minutes

1) 6:30 AM is 2 standard deviations above mean

P(employees are late on a typical day) = P(arrival is after 6:30 AM)

= 1 - P(arrival is before 6:30 AM)

= 1 - [P(arrival is before 6:26 AM) + P(arrival is between 6:26 AM and 6:30 AM)]

= 1 - [0.5 + 95/2]

= 0.025

= 2.5%

Percent of employees are late on a typical day = 2.5%

2) For an employee to arrive early enough to start work at 6:30 AM, an employee must report to work by 6:28 AM

P(arrival before 6:28 AM) = [P(arrival is before 6:26 AM) + P(arrival is between 6:26 AM and 6:28 AM)]

= 0.5 + 0.68/2

= 0.84

= 84%

Percent of this business employees arrive early enough to make this adjustment before the 6:30 A.M. start time = 84%