A livestock company reports that the mean weight of a group of young steers is 1100 pounds with a standard deviation of 93 pounds. Based on the model N (1100 ,93 ) for the weights of steers, what percent of steers weigh a) over 1050 pounds? b) under 1300 pounds? c) between 1150 and 1250 pounds?

a) Calculate the z-score.

z = (x - μ) / σ

z = (1050 - 1100) / 93

z = - 0.54

From a z-score table:

P (z<-0.54) = 0.2946

Therefore:

P (z>-0.54) = 1 - 0.2946

P (z>-0.54) = 0.7054

70.54% of steers are over 1050 pounds.

b) Calculate the z-score.

z = (x - μ) / σ

z = (1300 - 1100) / 93

z = 2.15

From a z-score table:

P (z<2.15) = 0.9842

98.42% of steers are under 1300 pounds.

c) Calculate the z-scores.

z = (x - μ) / σ

z = (1150 - 1100) / 93

z = 0.54

z = (1250 - 1100) / 93

z = 1.61

From a z-score table:

P (z<0.54) = 0.7054

P (z<1.61) = 0.9463

Therefore:

P (0.54
P (0.54
P (0.54
24.09% of steers weigh between 1150 pounds and 1250 pounds.