You have 500 data points, which are normally distributed with a mean of 400 and

Question

You have 500 data points, which are normally distributed with a mean of 400 and a standard deviation of 50. All scores are integers. Then one new data point is added, which is far above the top end of the distribution. (Thus, the new data point has the very highest score in the distribution, by a considerable margin.)

________H. What happens to the value of the z score of the new mean calculated using the 501 data points, compared to the value of the z score of the old mean calculated using the original 500 data points?

________I. What happens to the number of scores that are lower than 400?

________J. What happens to the number of scores that are higher than 400?

________K. What happens to the number of scores that are higher than 500?

________L. What happens to the number of scores that are higher than 700?

Explanation / Answer

Answers:

If we add one new data point to the original data and this new data point is far above the top end of the distribution, then mean of the distribution will be greater than 400. Also, the standard deviation will increase.

Part H

The value of the Z score of the new mean calculated using the 501 data points will be decreased as compared to the value of the z score of the old mean calculated using the original 500 data points because adding new data point will increase the standard deviation which will result in decreasing the z value.

Part I

For the original distribution of 500 data points, the number of scores which are lower than 400 and greater than 400 is the same because distribution is symmetric about mean 400. For the new distribution of 501 data points, z score will decrease and therefore the number of scores lower than 400 will also decrease.

Part J

As we discussed in the above part, the number of scores will decrease if we add a new data point which is far above the top end of the distribution. So, the number of scores higher than 400 will increase.

Part K

The number of scores higher than 500 will be increased because new mean will shift towards the right side and this will decrease z-score.

Part L

The number of scores higher than 700 will be increased because new mean will shift towards the right side and this will decrease z-score.

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