Problem 5. Pricing games An author of children’s online educational games wants

Question

Problem 5. Pricing games

An author of children’s online educational games wants to use statistics to decide on the price that each game should sell for. After surveying similar games sold by competitors, the author finds that the price of this type of games is normally distributed with a Mean price of $18.00 and a standard deviation of $4.25.

a.       If the author of the games wants to set a price, such that 90% of the competitors’ prices exceed the author’s price, what price should she set? Hint: Sketch a normal distribution graph that contains the information given in this question. [ 5 marks]

b.      If the author wants to price her games, so as to be in the middle 80% range of her competitors’ prices, what should the maximum game price be and what should the minimum game price be? Hint: Hint: Sketch a normal distribution graph that contains the information given in this question. [5 marks]

Explanation / Answer

a)as we know that for 90% of the competitors’ prices to exceed the author’s price ; Author's price should be at 10 percentile for whcih z =-1.2816

therefore corresponding price =mean +z*std deviation =18-1.2816*4.25 =$12.55

b) for middle 80% value fall between 10 and 90th percentile for which z =-/+ 1.2816

therfore minimum game price be =mean +z*std deviation =18-1.2816*4.25 =$12.55

and  maximum game price be =mean +z*std deviation =18+1.2816*4.25 =$23.45

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