A company's records indicate that on any given day, 1% of their day shift
employees and 2% of the night shift employees will miss work. Sixty percent of the employees
work the day shift.
a. What percent of employees are absent on any given day?
b. A randomly selected employee missed work today, what is the probability that he/she
is a night shift employee?
i don't even know where to start
percent=.01*.6 + .02*.4
.02*.4/(.02*.4+.01*.6)
No problem! I can help you break down the problem and guide you on how to find the answers.
Let's start with part (a):
a. What percent of employees are absent on any given day?
To find the percentage of employees absent on any given day, we need to consider both the day shift and night shift employees.
Given that 1% of the day shift employees and 2% of the night shift employees will miss work, we can calculate the overall percentage of employees absent by using the weighted averages.
First, calculate the percentage of employees who work during the day shift:
Percentage of day shift employees = 60%
Percentage of night shift employees = 100% - Percentage of day shift employees = 100% - 60% = 40%
Now, calculate the overall percentage of employees absent:
Overall percentage of absent employees = (Percentage of day shift employees * Absent rate for day shift) + (Percentage of night shift employees * Absent rate for night shift)
= (60% * 1%) + (40% * 2%)
Simplifying the equation:
Overall percentage of absent employees = 0.6% + 0.8%
= 1.4%
Therefore, the overall percentage of employees absent on any given day is 1.4%.
Moving on to part (b):
b. A randomly selected employee missed work today, what is the probability that he/she is a night shift employee?
To answer this question, we'll use conditional probability. The probability that the selected employee is a night shift worker given that they missed work can be calculated using Bayes' theorem.
Let's denote the following:
A: Event that the employee is a night shift worker
B: Event that the employee missed work today
We want to find P(A|B), the probability that the employee is a night shift worker given that they missed work. We can use Bayes' theorem:
P(A|B) = [P(B|A) * P(A)] / P(B)
P(B|A), the probability that the employee missed work given that they are a night shift worker is given as 2%.
P(A) is the probability that the randomly selected employee is a night shift worker, which we calculated earlier as 40%.
To find P(B), the probability that an employee missed work today, we need to consider both day shift and night shift workers. We can calculate it using the law of total probability:
P(B) = P(B|A) * P(A) + P(B|A') * P(A')
P(B|A'), the probability that the employee missed work given that they are a day shift worker, is 1%.
P(A') is the probability that the selected employee is a day shift worker, which can be calculated as 100% - P(A) = 100% - 40% = 60%.
Now, we can plug these values into the equation to find P(B):
P(B) = (2% * 40%) + (1% * 60%)
= 0.8% + 0.6%
= 1.4%
Finally, we can calculate P(A|B) using Bayes' theorem:
P(A|B) = [P(B|A) * P(A)] / P(B)
= (2% * 40%) / 1.4%
= 0.8% / 1.4%
= 0.5714 (approximately)
Therefore, the probability that the randomly selected employee who missed work today is a night shift worker is approximately 57.14%.