Statistics question HELP

Question

Every year "Nathan's hotdog stand of Coney Island NY holds a hot dog eating contest. Assume the that number of hot dogs eaten by contestants last year was normally distributed with a mean of 40 and a standard deviation of 5.

What percentage of contestants ate between 45 and 50 hot dogs?

(Multiply by 100 and THEN use 2 decimals)

Explain step by step

Answer 1

In order to use the normal probability density curve, you need to find the z-score for the lowest value and the z-score for the highest value. The lowest value z-score is found by subtracting the population mean from the low value and then dividing by the standard deviation (z=(45-40)/5). The low z-score = 1 and the upper z-score is (z=(50-40)/5) z = 2.

Therefore, you need to find the area in the z-table for z = 2 (0.9772) and the area for z = 1 (0.8413).

Now, subtract the smaller area from the larger area. (0.9772 - 0.8413 = 0.1359).

The answer is 13.59%.

I hope that helps you.