Z-score Review Name:

1. The grades on a history test are normally distributed with μ=85andσ=4.5.

a)  Draw a normal curve. Label ±1, ±2, and ±3 standard deviations.

b)  What did the middle 68% of students score on the history test?

c)  What percentage of students scored 71.5 points or below?

d)  What percentage of students scored above a 94?

e)  What percentage of students scored between 83 and 90?

f)  40% of students scored at or below what score?

2. The scores on a statewidelanguageexam were normally distributed withμ=72.20andσ=6.Michaelscored77on the exam. Michael's exam grade was higher than what percentage of test-takers?

3. A patient recently diagnosed with Alzheimer's disease takes a cognitve abilities test. The patient scores a 45 on the test (mean = 52, standard deviation of 5). What is this patient's percentile rank?

4. Pat and Chris both took a spatial abilities test (mean = 80, S = 8). Pat scored a 76 and Chris scored a 94. What percent of individuals would score between Pat and Chris?

5. The weight of chocolate bars from a particular chocolate factory has a mean of 8 ounces with standard deviation of .1 ounce.

a. What percentage of chocolate bars weigh between 7.9 and 8.2 ounces?

b. What percentage of chocolate bars weigh more than 8 ounces?

c. 32% of chocolate bars weigh less than how many ounces?

d. What is an 8.05 ounce candy bars’ percentile?

e. What percent of candy bars weigh more than 7.95 ounces?

6. A group of friends compares what they received while trick or treating. They find that the average number of pieces of candy received is 43, with standard deviation of 4.

a.  What is thez-score corresponding to 23 pieces of candy?

b.  How likely to happen is the outcome in part a?

c.  You received 52 pieces of candy. What percentage of friends received less candy than you?

d.  How likely is it to receive 38 pieces of candy?

7. Professor Halen has 184 students in his college mathematics lecture class. The scores on the midterm exam arenormally distributedwith a mean of 72.3 and a standard deviation of 8.9. How many students in the class can be expected to receive a score between 81 and 89? Express answer to thenearest student.

8. Five children aged 2, 3, 5, 7, and 8 years old weigh 14, 20, 32, 42, and 44 kilograms respectively.

a. Find the equation of the regression line of age vs weight.

b. Based on this data, what is the approximate weight of a six-year-old child?

c. Create a new data point that would make the slope of the regression line as close to zero as possible.

d. Create a new data point that would NOT change the regression line equation.

9. Students were surveyed on the number of hours devoted each day to sleeping and watching TV. The responses are summarized in the table.

Hours of TV / 5 / 5 / 4 / 4 / 3 / 3 / 2 / 1
Hours Sleeping / 3.5 / 4 / 5 / 6 / 5.5 / 7 / 7 / 8

a.  Create a scatter plot for the data.

b.  Determine the Centroid.

c.  Write your own Best-Fit-Line.

d.  Use your calculator to determine the Least-Squares-Regression line.

e.  How do your lines compare?

f.  What is the correlation coefficient?

g.  What does the correlation coefficient tell you about the number of hours watching TV vs the number of hours spent sleeping?

10. Estimate the correlation coefficient for the graphs below.

11. Draw a picture of a scatter plot that would have an approximate correlation coefficient of .65.

12. Draw a picture of a scatter plot that would have an approximate correlation coefficient of .25.