Question

QUESTION 2  

According to Michael Theatre Ltd., the mean cost to run a nightly theatre performance is $3,200 with a standard deviation of $460. Performance costs are known to follow a normal probability distribution.

Required:

1. What percentage of the performances will cost less than $2,850 to run? Sketch a normal curve and shade the desired area on your diagram. ( 4 marks)
2. What percentage of the performances will cost between $3,250 and $3,520 to run? Sketch a normal curve and shade the desired area of your diagram. ( 4 marks)
3. What percentage of the performances will cost between $2,300 and $3,520 to run? Sketch a normal curve and shade the desired area on your diagram. ( 4 marks)
4. What percentage of the performances will cost less than $3,750 to run? Sketch a normal curve and shade the desired area of your diagram. Also, Six percent (6 %) of all shows will cost less than what dollar amount? Sketch a normal curve and shade the desired area of your diagram. ( 8 marks)

I Need the full calculation and explanation of the answers.

Answer 1

We are given that the mean performance cost =$3200 and =$460. We know that any Normal distribution can be transformed to a standard normal variate by the transformation

a. Percentage of the performances will cost less than $2,850 to run =   

  

  Percentage of the performances will cost less than $2,850 to run

We can either look into the table(Fisher & Yates) or use the EXCEL function.NORM.S.DIST(-0.7609,TRUE).

  . ie 22.34% of the performances will cost less than $2850.

b.Percentage of the performances will cost between $3,250 and $3,520 to run

For $3250,   

For $3520,   

  Percentage of the performances will cost between $3,250 and $3,520 to run

This can be calculated by

   Percentage of the performances will cost between $3,250 and $3,520 to run=0.2131 or 21.31%

c. Percentage of the performances will cost between $2,300 and $3,520 to run

For $2300,

For $3520,

Percentage of the performances will cost between $2,300 and $3,520 to run

Percentage of the performances will cost between $2,300 and $3,520 to run =0.7315 or 73.15%.

d.Percentage of the performances will cost less than $3,750 to run

     

  Percentage of the performances will cost less than $3,750 to run

or 88.41%

Percentage of the performances will cost less than $3,750 to run=88.41%

e.Six percent (6 %) of all shows will cost less than what dollar amount. here we need to first find out that Z for which

  

This will be obtained by the Inverse Normal function to find the ordinate. NORM.S.INV(0.06) in Excel or the Table 1 of the Fisher & Yates. which is -1.5548

  

  

  

Six percent (6 %) of all shows will cost less than $2485.