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wrote...
Posts: 200
3 weeks ago
At a large business, employees must report to work at 7:30 A.M. The arrival times of employees can be described by a Normal model with mean of 7:22 A.M. and a standard deviation of four minutes.

a. What percent of employees are late on a typical work day?
b. A psychological study determined that the typical worker needs five minutes to adjust to their surroundings before beginning their duties. What percent of this business’ employees arrive early enough to make this adjustment?
c. Because late employees are a distraction and cost companies money, all employees need to be on time to work. If the mean arrival time of employees does not change, what standard deviation would the arrival times need to ensure virtually all employees are on time to work?
d. Explain what achieving a smaller standard deviation means in the context of this problem.
Textbook 

Stats: Modeling the World


Edition: 4th
Authors:
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3 weeks ago
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a. Employees are late if they arrive after 7:30 A.M.
   P(time > 7:30) = P(z > = 2) = 0.0228
    According to the Normal model, about 2.28% of employees are expected to arrive after 7:30 AM.

b. P(x ≤ 25) = P(z < = 0.75) = 0.773
    According to the Normal model, about 77.3% of employees arrive at work before 7:25 AM.


c. Virtually all times lie within 3 standard deviations of the mean. (Accept other reasonable z-scores greater than 3).  If z = 3 ≤ , then 3σ ≤ 8, so σ≤ 2.67 minutes.
d. A smaller standard deviation would mean greater consistency in arrival times.
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wrote...
3 weeks ago
Good timing, thanks!
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