Question

A livestock company reports that the mean weight of a group of young steers is 1149 pounds with a standard deviation of 89 pounds. Based on the model ​N(1149​,89​) for the weights of​ steers, what percent of steers weigh ​a) over 1150 ​pounds? ​b) under 1250 ​pounds? ​c) between 1100 and 1200 ​pounds?

Answer 1

Answer:

Given,

Mean = 1149

Standard deviation = 89

a)

Over 1150

P(X > 1150) = P((x-mu)/s > (1150 - 1149)/89)

= P(z > 0.01)

= 0.4960106 [since from z table]

= 0.4960

b)

Under 1250

P(X < 1250) = P((x-mu)/s < (1250 - 1149)/89)

= P(z < 1.13)

= 0.8707619 [since from z table]

= 0.8708

c)

Between 1100 and 1200 ​pounds

P(1100 < X < 1200) = P((1100 - 1149)/89 < (x-mu)/s < (1200 - 1149)/89)

= P(-0.55 < z < 0.57)

= P(z < 0.57) - P(z < -0.55)

= 0.7156612 - 0.2911597 [since from z table]

= 0.4245