Question

The weights in pounds of a breed of yearling cattle follows the Normal model

​N(1128​,62​).

What weight would be considered unusually low for such an​ animal?

Select the correct choice below and fill in the answer boxes within your choice.

A.Any weight more than 2 standard deviations below the​ mean, or less than

nothing

​pounds, is unusually low. One would expect to see a steer 3 standard deviations below the​ mean, or less than

nothing

pounds only rarely.

B.Any weight more than 3 standard deviations below the​ mean, or less than

nothing

​pounds, is unusually low. One would expect to see a steer 2 standard deviations below the​ mean, or less than

nothing

pounds only rarely.

C.Any weight more than 1 standard deviation below the​ mean, or less than

nothing

​pounds, is unusually low. One would expect to see a steer 2 standard deviations below the​ mean, or less than

nothing

pounds only rarely.

Answer 1

Solution:

The probability is said to be unusual if it is less than 5% i.e. less than 0.05

Given the normal distribution with   = 1128 and    = 62

According to the Empirical rule there is 95% chance that the observation lie within 2 standard deviations from the mean.

There is 5% chance that weight will be below  - 2 or above   + 2

The weights that are below - 2 are considered as Unusually low.

- 2 = 1128 - (2 * 62) = 1004

   - 3 = 1128 - (3 * 62) = 942

Answer :

A. Any weight more than 2 standard deviations below the mean or less than 1004 pounds , is unusually low.One would expect to see a steer 3 standard deviations below the mean or less than 942 pounds is only rarely.

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