Question

The weight of Los Angeles Dodgers players is normally distributed with a mean of 203 pounds and a standard deviation of 18 pounds. (30 points) (show all calculations; round to fourth decimal place)

A. What percent of players weigh between 190 and 216 pounds? (10 points)

B. Albert’s weight is among the top 10%. What is his minimum weight? (10 points)

Answer 1

Solution :

Given that ,

mean = = 203

standard deviation = = 18

A) P(190 < x < 216) = P[(190 - 203)/ 18) < (x - ) /  < (216 - 203) / 18) ]

= P(-0.7222 < z < 0.7222)

= P(z < 0.7222) - P(z < -0.7222)

Using z table,

= 0.7649 - 0.2351

= 0.5298

percent = 52.98%

B) Using standard normal table,

P(Z > z) = 10%

= 1 - P(Z < z) = 0.10  

= P(Z < z) = 1 - 0.10

= P(Z < z ) = 0.90

= P(Z < 1.2816 ) = 0.90

z = 1.2816

Using z-score formula,

x = z * +

x = 1.2816 * 18 + 203

x = 226.0688

minimum weights = 226.0688 pounds.