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Annual entertainment expenses in a population of 100 families have a mean of $2040 and a standard deviation of $360.
(a) Find the mean and standard deviation of monthly expenses.
(b) What is the total amount of monthly entertainment expenses for this population?

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Answer:

The correct answer is:

(a) Mean = 170,

    Standard deviation = 30

(b) 1700

Step-by-step explanation:

Given:

  • n = 100
  • μ = 2040
  • σ = 360

(a)

Mean of monthly expenses will be:

= [tex]\frac{\mu}{2}[/tex]

= [tex]\frac{2040}{2}[/tex]

= [tex]170[/tex]

Standard deviation will be:

= [tex]\frac{\sigma}{12}[/tex]

= [tex]\frac{360}{12}[/tex]

= [tex]30[/tex]

(b)

The total amount of monthly expenses will be:

= [tex]n\times \frac{\mu}{12}[/tex]

= [tex]100\times 170[/tex]

= [tex]1700[/tex]

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