The Virginia Cooperative Extension reports that the mean weight of yearling ANgu

Question

The Virginia Cooperative Extension reports that the mean weight of yearling ANgus steers is 1152 pounds. Suppose that the weights of all such animals can be described by a normal model with a mean of 1152 pounds as stated, and a standard deviations of 84 pounds. Answer the following based on that model. For parts a through f, your answer should include a sketch of the distribution showing the mean and the area of interested shaded and the calculation itself.

a) What proportion of Angus steers weighs more than 1400 pounds?

b) What proportions of Angus steers weighs less than 1202 pounds?

c) What proportion of Angus steers weighs between 88 and 1075 pounds?

d) What is the value for Q1 for the weights?

e) A rancher wants to examine the smallest 20% of his herd. What is the corresponding cutoff weight?

f) A particular buyer wants to purchase the largest 15% of the herd. What is the corresponding cutoff weight?

g) Based on z scores, which would be more unusual, a steer weighing 1000 pounds of one weighing 1250 pounds? NO sketch needed.

h) Sketch the distribution for the weight of these cattle showing the mean and the weights corresponding to the 68-95-99.7 rule.

i) What are the individuals? What is the response variable and its units and type?

Explanation / Answer

a. P(x>1400)=P(z>1400-1152/84)=P(z>2.95)=0.0016

b. P(x<1202)=P(z<0.595)=0.7241

c. P(880<x<1075)=P(-3.2<z<-0.92)=0.1781

d. z = (x - µ)/

-0.6745 = (x -1152)/84

x =1095.342 (first quartile)

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