The mean weight of a breed of yearling cattle is 1065 pounds. suppose that weights of all such animals can be described by the normal model n(1065,56). a) how many standard deviations from the mean would a steer weighing 1000 pounds be? b) which would be more unusual, a steer weighing 1000 pounds, or one weighing 1250 pounds?

a)

And this value means that the weight X=1000 pounds it's 1.6 deviations below the true mean of 1065 pounds

b)

And this value means that the weight X=1250 pounds it's 3.304 deviations above the true mean of 1065 pounds.

So we can cocnlude on this case that the weight of 1250 would me more unusual since represent a value with a more distance respect to the mean than the weight of 1000 pounds.

Step-by-step explanation:

1) Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".  

2) Part a

Let X the random variable that represent the weights of a breed of yearling cattle of a population, and for this case we know the distribution for X is given by:

Where and

And the best way to solve this problem is using the normal standard distribution and the z score given by:

If we find the Z score for the value of X=1000 we got:

And this value means that the weight X=1000 pounds it's 1.6 deviations below the true mean of 1065 pounds

3) Part b

For this case if we find the z score for the value of 1250 we got:

And this value means that the weight X=1250 pounds it's 3.304 deviations above the true mean of 1065 pounds.

So we can cocnlude on this case that the weight of 1250 would me more unusual since represent a value with a more distance respect to the mean than the weight of 1000 pounds.