Question

A livestock company reports that the mean weight of a group of young steers is 1077 pounds with a standard deviation of 66 pounds. Based on the model ​N(1077​,66​) for the weights of​ steers, what percent of steers weigh

​a) over 1300 ​pounds?

​b) under 1050 ​pounds?

​c) between 1000 and 1200 ​pounds?

a) __ ​% of steers have weights above 1300 pounds.

​(Round to one decimal place as​ needed.)

​b) __ % of steers have weights below 1050 pounds.

​(Round to one decimal place as​ needed.)

​c) __ % of the steers weigh between 1000 and 1200 pounds.

​(Round to one decimal place as​ needed.)

Answer 1

Solution :

Given that ,

mean = = 1077

standard deviation = = 66

a) P(x > 1300) = 1 - p( x< 1300)

=1- p P[(x - ) / < (1300 - 1077) / 66 ]

=1- P(z < 3.38)

Using z table,

= 1 - 0.9996

= 0.0004

0.04% of steers have weights above 1300 pounds.

b) P(x < 1050) = P[(x - ) / < (1050 - 1077) / 66]

= P(z < -0.41)

Using z table,

= 0.3409

34.1% of steers have weights below 1050 pounds.

c) P(1000 < x < 1200) = P[(1000 - 1077)/ 66 ) < (x - ) /  < (1200 - 1077) /66 ) ]

= P(-1.17 < z < 1.86)

= P(z < 1.86) - P(z < -1.17)

Using z table,

= 0.9686 - 0.1210

= 0.8476

84.8% of the steers weigh between 1000 and 1200 pounds.