Question

A livestock company reports that the mean weight of a group of young steers is 1168 pounds with a standard deviation of 74 pounds. Based on the model ​N(1168,74) for the weights of steers, what percent of steers weigh

a) over 1200 ​pounds? ​

b) under 1100 ​pounds? ​

c) between 1000 and 1050 ​pounds?

Answer 1

Solution:
Given in the question
Mean = 1168
Standard deviation = 74
and this is normally distributed
Solution(a)
P(Xbar>1200) = 1-P(Xbar<1200)
Z = (1200-1168)/74 = 32/74 = 0.4324
From Z table we Found p-value
P(Xbar>1200) = 1- 0.6664=0.3336
SO there is 33.36% probabilitty tat weight is over than 1200 pounds
Solution(b)
P(Xbar<1100) =?
Z = 1100-1168 / 74 = -0.9189
from the z table we found p-value
P(Xbar<1100) = 0.1788
So ther is 17.88% probability
Solution(c)
P(1000<Xbar<1050) = P(Xbar<1050)-P(Xbar<1000)
Z = 1050-1168 / 74 = -1.5945
Z = 1000-1168 /74 = -2.270
P(1000<Xbar<1050) = 0.0548 - 0.0116 = 0.0432 or 4.32%