Question

The weights of professional wrestlers are approximately normally distributed with a mean of 220 pounds and a standard deviation of 7 pounds. Using the normalcdf function on your graphing calculator, approximately what percent of wrestlers have weights less than 205 pounds?

Answer 1

1.6%

Explanation:

The cumulative distribution function (CDF) of a random variable X is denoted by F(x), and is defined as

F(x) = P(X ≤ x). where x is the largest possible value of X that is less than or equal to x

z = (x-μ)/σ,

where:

x is the raw score = 205

μ is the population mean, = 220 pounds

σ is the population standard deviation = 7 pounds

205 -220/7

z = -15/7

z = -2.1428571429

Using the normal cdf function on your graphing calculator,the cumulative distribution is

normalcdf( -2.1428571429, 100)

= 0.01606229

In percent form = 0.01606229 × 100

= 1.6%