Problem

You want to know the percentage of medical equipment companies that earned revenue greater than 87 million dollars. If the mean revenue was 50 million dollars and the data has a standard deviation of 15 million, find the percentage. Assume that the distribution is normal. Round your answer to the nearest hundredth.

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Final Answer: The percentage of medical equipment companies that earned revenue greater than 87 million dollars is approximately \(\boxed{32\%}\).

Steps

Step 1 :Given that the mean revenue is \(50\) million dollars and the standard deviation is \(15\) million dollars, we want to find the percentage of companies that earned more than \(87\) million dollars.

Step 2 :We can use the z-score formula to find the z-score for \(87\) million dollars. The z-score is a measure of how many standard deviations an element is from the mean.

Step 3 :Calculate the z-score using the formula \(z = \frac{x - \text{mean}}{\text{std_dev}}\). Substituting the given values, we get \(z = \frac{87 - 50}{15} = 2.47\).

Step 4 :Once we have the z-score, we can use a z-table to find the percentage of companies that earned more than \(87\) million dollars. The z-table gives us a percentage of \(0.68\).

Step 5 :However, since we are looking for the percentage of companies that earned more than \(87\) million dollars, we need to subtract this value from \(1\) (since the total probability is \(1\) or \(100\%\)).

Step 6 :So, the percentage of companies that earned more than \(87\) million dollars is \(1 - 0.68 = 0.32\) or \(32\%\).

Step 7 :Final Answer: The percentage of medical equipment companies that earned revenue greater than 87 million dollars is approximately \(\boxed{32\%}\).

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