Question

A livestock company reports that the mean weight of a group of young steers is 1125 pounds with a standard deviation of 91 pounds. Based on the model ​N(1125​,91​) for the weights of​ steers, what percent of steers weigh ​a) over 1150 ​pounds? ​b) under 900 ​pounds? ​c) between 1050 and 1300 ​pounds?

Answer 1

Answer

we have

(A) probability over 1150 pounds, x(bar) = 1150

using the formula

setting the given values, we get

Using the identity

using z distribution table, we get

converting to %, 0.3936*100 = 39.36%

(B)

probability under 900 pounds, x(bar) = 900

using the formula

setting the given values, we get

Using the identity

using z distribution table, we get

converting to %, 0.0068*100 = 0.68%

(C) probability between 1050 and 1300 pounds, x(bar)1 = 1050 and x(bar)2 = 1300

using the formula

setting the given values, we get

Using the identity

using z distribution table, we get

converting to %, 0.7665*100 = 76.65%