Question

What is the human resource cost of hiring and maintaining employees in a company? Studies conducted by Saratoga Institute, Price-Waterhouse-Coopers Human Resource Services, determined that the average cost of hiring and employee is $3,270, and the average annual human resource expenditure per employee is $1,554. The average health benefit payment per employee is $6,393, and the average employer 401(k) cost per participant is $2,258. According to a survey conducted by the American Society for Training and Development, companies annually spend an average of $955 per employee on training, and, on average, an employee receives 32 hours of training annually. Business researchers have attempted to measure the cost of employee absenteeism to an organization. A survey conducted by CCH, Inc. showed that the average annual cost of unscheduled absenteeism per employee is $660. According to this survey, 35% of all unscheduled absenteeism is caused by personal illness.

1. The survey conducted by the American Society for Training and Development reported that, on average, an employee receives 32 hours of training per year. Suppose that the number of hours of training is uniformly distributed across all employees varying from 0 hours to 64 hours.
   1. What percentage of employees receive between 20 and 40 hours of training?

2. What percentage of employees receive 50 hours or more of training?

2. As the result of another survey, it was determined that, on average, it costs $3,270 to hire an employee. Suppose such costs are normally distributed with a population standard deviation of $400.
   1. Based on these figures, what is the probability that a randomly selected hire costs more than $4,000?

(Could this done with no calculus to make sure my answer matches up with the work I did, thank you)

Answer 1

A)

here a=   0
b=   64

employees receive between 20 and 40 hours of training=

x1 =   20              
x2=   40              
                  
P (    20   ≤ X ≤    40   ) =(x2-x1)/(b-a) =    0.3125 = 31.25%

employees receive 50 hours or more of training=

P(X ≥ x) =   (b-x)/(b-a) =    0.2188 = 21.88%

B)

µ =    3270                  
σ =    400                  
                      
P ( X ≥   4000.00   ) = P( (X-µ)/σ ≥ (4000-3270) / 400)              
= P(Z ≥   1.825   ) = P( Z <   -1.825   ) =    0.0340

   excel formula for probability from z score is =NORMSDIST(Z)                  

Please revert back in case of any doubt.

Please upvote. Thanks in advance.