## Question 320:

1

Calculate a z-score for the desired score. (90-84.2)/12.8 = .4531. Now lookup the one-sided area using the z-score to percentile calculator and look at the 1-sided area. You should get an area of 67.7%. You need to think about what the question is asking to know to use the larger of the area. Since the score of 90 is above the mean of 84.2, we know the area must be greater than 50%.

For the second questions I'm assuming they want you to use the t-distribution since the sample size is reasonably small. Use the Excel formula =TDIST(0.4531,19,1) where you use the parameters of the z-score, the degrees of freedom, which for this test are 1 less than the sample size and the last parameter is the 1-sided option. You should get .327, and then 1 minus this is 67.2%. So using the t-distribution instead of the normal (often called the z-distribution) you have a difference of .5% (67.7 vs. 67.2).

Be sure to look at the interactive graph of the standard normal curve and enter the mean of 84.2 and standard deviation of 12.8. Look at the 1-sided area graph and you can see the area corresponding the the score of 90.