Question

A livestock company reports that the mean weight of a group of young steers is 1145 pounds with a standard deviation of 84pounds. Based on the model ​N(1145,84​) for the weights of​ steers, what percent of steers weigh ​

a) over 1050 ​pounds? ​

b) under 1000​pounds? ​

c) between 1250 and 1300 ​pounds?

Answer 1

Solution :

a.

P(x > 1050) = 1 - P(x < 1050)

= 1 - P[(x - ) / < (1050 - 1145) / 84)

= 1 - P(z < -1.13)

= 1 - 0.1292

= 0.8708

Percent = 87.08%

b.

P(x < 1000) = P[(x - ) / < (1000 - 1145) / 84]

= P(z < -1.73)

= 0.0418

Percent = 4.18%

c.

P(1250 < x < 1300) = P[(1250 - 1145)/ 84) < (x - ) /  < (1300 - 1145) / 84) ]

= P(1.25 < z < 1.85)

= P(z < 1.85) - P(z < 1.25)

= 0.9678 - 0.8944

= 0.0734

Percent = 7.34%