Introduction to Statistics

Advanced P-Value Worksheet: Solutions Name _____________________________

1. On a practical nursing exam, the mean is 79 and std. dev. is 9. Find the test scores related to the area in the charts below:

a. Upper 80% b. Middle 50%

Use invNorm(.2,79,9) Use invNorm(.25,79,9) & invNorm(.75,79,9)

p=.2, X=71.4 p=.25, X=72.9 and p=.75, X=85.1

2. For the standard normal curve, find the test scores related to the area in the charts below:

a. Middle 50% b. Middle 80%

Use invNorm(.25,0,1) Use invNorm(.1,0,1) & invNorm(.9,0,1)

p=.25, Z=-.67 and p=.75, Z=.67 p=.1, Z= -1.28 and p=.9, Z=1.28

3. On the practical nursing exam (mean is 79, std. dev. is 9), scores of 75 and higher are considered passing. Find the percent of students that pass and mark the appropriate areas on the figure below:

X=75 (use z-test w/ > ineq): p=.6716

4. The entrance exam scores for a private high school are converted to standardized Z-scores. Only Z-scores of 1.25 and higher are considered for admission. What percent of applicants are eligible? Draw and shade the appropriate areas below:

Z=1.25 (use z-test w/ > ineq): p=.1056

Police response time in Denver has a normal distribution where the mean is 8.4 minutes and the std. dev. is 1.7. Use the blank templates below to sketch the region indicated, and find all requisite p-values and X-values.

5. P(5 < X < 10)

“between 5 and 10 min.”

X=5 and X=10 (use z-test 2x w/ < ineq):

p=.0228 and p=.826

answer = 80.39% (subtract p’s)

6. P(X < 6)

“less than 6 min.”

X=6 (use z-test w/ < ineq):

p=.079

answer = 7.9%

7. The “Middle 60%”

of response times.

p=.2 and p=.8 (use invNorm twice):

X=6.97 and X=9.83

Answer: “Between 6.97 and 9.83 minutes”

8. The “Upper Quartile”

of response times.

p=.75

use invNorm(.75,8.4,1.7):

X=9.55