I have the answers, but, how do you figure the math? A livestock company reports
ID: 3205516 • Letter: I
Question
I have the answers, but, how do you figure the math?
A livestock company reports that the mean weight of a group of young steers is 1106 pounds with a standard deviation of 67 pounds. Based on the model N(1106,67) for the weights of steers, what percent of steers weigh a) over 1300 pounds? b) under 1000 pounds? c) between 1200 and 1250 pounds? a) 0% of steers have weights above 1300 pounds. (Round to one decimal place as needed.) b) 5.7% of steers have weights below 1000 pounds. (Round to one decimal place as needed.) c) 6.5% of the steers weigh between 1200 and 1250 pounds. (Round to one decimal place as needed.)Explanation / Answer
Mean m = 1106
Standard deviations sd= 67
P(x>1300) = 1-P(x<1300)
= 1 - P(z=(x-m)/sd)
= 1 - P(z= (1300-1106)/67)
= 1 - P(z=2.9)
= 1 - 0.9981 (from standard normal distribution table)
= 0.0019
B) P(x<1000)
= P(z=(1000-1106)/67)
= P(z= -1.58)
= 0.0571 = 5.7%
C) P(1200<x<1250)
= P(x<1250) - P(x<1200)
= P(z = (1250-1106)/67)) - P(z= (1200-1106)/67)
= P(z= 2.15) - P(z= 1.4)
= 0.9842-0.9192
= 0.0650
= 6.5%