Publishing company

Suppose you work for a publishing company, and before launching a new magazine targeting fashion-oriented consumers, your boss wants to hold a meeting with prospective advertisers. Assume that annual expenditures on magazine ads in this genre are normally distributed with a mean of $498,566 and a standard deviation of $43,800. Suppose the publisher wants to exclude companies with the smallest 7.78% in terms of annual expenditures on magazine ads from the sales meeting. What is the approximate minimum yearly expenditure on magazine ads an advertiser would be required to have so that advertiser would be invited to the meeting? (Hint: What z score corresponds to the minimum expenditure for advertisers that should be invited?)

Correct answer:

x =  436370

Step-by-step explanation:

$$\begin{gathered} \mu =498566\text{USD} \\ \sigma =43800\text{USD} \\ p=7.78\%=\frac{7.78}{100}=0.0778 \\ {p}_2=1/2-p=1/2-0.0778=0.4222 \\ z-score \\ z=1.42 \\ z=\frac{x\mp \mu }{\sigma } \\ x=\mu -\sigma \cdot z=498566-43800\cdot 1.42=436370 \end{gathered}$$

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