contestada

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.

Respuesta :

adelekeademolu

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%.

The percentage of employees that are late on a typical day in the company is 2.5%

How to calculate percentage?

From the information given, it was stated that half of the employees arrive between 7.14 am and 7.30am. This implies that those the percentage will be:

= 95%/2

= 47.5%

Therefore, the late arrivals will be:

= 50% - 47.5%

= 2.5%

Also, the percentage of the employees who arrive before 7.26 am will be:

= 50% + (68%/2)

= 50% + 34%

= 84%

Therefore, the percentage of the employees who arrive before 7.26 am is 84%.

Learn more about percentages on:

https://brainly.com/question/24877689

Otras preguntas