Question

3. An athletic association wants to sponsor a footrace. The average time it takes to run the course is 58.6 minutes, with a standard deviation of 4.3 minutes. If the association decides to include only the top 15% of the racers, what should the cutoff be in the tryout run? Assume the variable is normally distributed.

4. An automobile dealer finds that the average price of a previously owned vehicle is $8,256. He decides to sell cars that will appeal to the middle 60% of the market in terms of price. Find the maximum and minimum prices of the cars the dealer will sell. The standard deviation is $1,150 and the variable is normally distributed.
   

5. An advertising company plans to market a product to low-income families. A study states that for a particular area, the average income per family is $44,596 and the standard deviation is $16,256. If the company plans to target the bottom 18% of the families based on income, find the cutoff income. Assume the variable is normally distributed.

PLEASE EXPLAIN

Answer 1

Answer:

We want to find what z-value 15% of the data to the left is of.

From the table, the closest z-score to p = 0.15 is z = -0.88

Converting x to z we have

-0.88 = x-58.6/4.3

=54.816

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