Question 714:

Asked on May 5, 2009

Tags: Z-Score

1

Answer:

No answer provided yet.For part 1 of this question we can use the properties of the normal curve and the properties of confidence intervals. We can do some quick math and see that for the 1st part of the question the values of 40 and 60 are 1 standard deviation above and below the mean. We know that 68% of values fall within this range so this would be the best answer given the information provided. 

Note: This is a poorly worded question as it mixes a few concepts. In actuality, the probability the population mean will fall between 40 and 60 is far more than 68%. Unfortunately we don't know what the sample size of the high-school or population are to properly calculate the standard error of the mean. It's important to know that the 68% probability is for any value, not the mean. The mean will be much closer to 50, but without more information its impossible to answer this question.

For part 2 we just need to lookup these values in a normal table using the percent of area to find the z-score or critical values. We can also use the excel formula =NORMSINV().  We get:

1. .05 two tailed = 1.9599
2. .02 right tailed (=98% CI) = 2.053749
3. .10 left tail = -1.28155
4. .10 two tailed = 1.644854