C5.5: Suppose that the weights of all such animals can be described by a Normal model with a standard deviation of 98 pounds.

Question

A livestock cooperative reports that the mean weight of yearling Angus steers is

1147 pounds. Suppose that the weights of all such animals can be described by a Normal model with a standard deviation of 98 pounds.

​a) What percent of steers weigh over 1100 ​pounds?

​b) What percent of steers weigh under 950 ​pounds?

​c) What percent of steers weigh between 1150 and 1300 ​pounds?

Answer 1

x weight is N(1147,98), mean 114 SD 98

a) want to find P(x > 1100)

P(x > 1100) = P(z > (1100 - mean/SD)) = P(z > (1100 - 1147)/98) = P(z > -0.48) = 1 - P(z < -0.48) = 1 - 0.3156 = 0.6844 = 68.44%

b) want to find P(x < 950)

P(x < 950) = P(z < (950-1147)/48) = P(z < -4.1) ~ 0%

c) want to find P(1150 < x < 1300) = P( (1150-1147)/98 < z < (1300 - 1147)/98) + P(0.03 < z < 1.56) = P(z < 1.56) - P(z < 0.03) = 0.9406 - 0.512 = 0.4286