Question

1. XYZ Manufacturing Company buys 50 tons of coal per month. The price of 50 tons of coal can vary from month to month according to the table shown below:

Price of 50 Tons of Coal	Probability
$1500	0.20
$2000	0.50
$2500	0.30

How much should XYZ budget for coal in 2020? Your answer should be an integer.

2.

Replacement times for computer displays players are normally distributed with a mean of 7.1 years and a standard deviation of 1.4 years.

If you want to provide a warranty so that only 2% of the computer displays will be replaced before the warranty expires, what is the time length of the warranty? Include 1 decimal place in your answer.

3. The amount of time a person waits for an elevator in a building is known to follow a uniform distribution between 0 and 60 seconds. What is the expected value of the wait time for an elevator? Your answer should be an integer. What is the probability that a person will wait between 20 and 35 seconds? Include 2 decimal laces in your answer.

Answer 1

2)

µ=   7.1                  
σ =    1.4                  
proportion=   0.9800                  
                      
Z value at    0.98   =   2.054   (excel formula =NORMSINV(   0.98   ) )
z=(x-µ)/σ                      
so, X=zσ+µ=   2.054   *   1.4   +   7.1  
X   = 10.0 years (answer)          

3)it is uniform distribution   
  
here a=   0
b=   60

a)  expected value of the wait time for an elevator=mean =    (a+b)/2 =    30 seconds

b) P (    20   ≤ X ≤    35   ) =(x2-x1)/(b-a) = (35-20)/60-0)= 0.25 seconds