Question

Suppose the weights of sumo wrestlers are normally distributed with a mean of 330lbs and a standard deviation of 15lbs. An up and coming competitor wants to defeat wrestlers whose weights are in the top 10%. What is the minimum weight of the sumo wrestlers at the highest weight of the league? Round your answer to the nearest whole number, if necessary.

Answer 1

Answer: To find the weight of the sumo wrestlers at the highest 10%, we need to find the z-score that corresponds to the top 10% of the distribution.

Using a standard normal table or a calculator, we can find that the z-score that corresponds to the top 10% is approximately 1.28.

Next, we can use the formula for a z-score to find the weight that corresponds to this z-score:

z = (x - mu) / sigma

where z is the z-score, x is the weight we want to find, mu is the mean weight, and sigma is the standard deviation.

Substituting in the values we know, we get:

1.28 = (x - 330) / 15

Solving for x, we get:

x = 1.28(15) + 330 = 349.2

Rounding to the nearest whole number, the minimum weight of the sumo wrestlers at the highest weight of the league is 349 lbs.

Explanation: