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Chapter 2 Review Name: ______________________
Use the following information to answer questions 1 – 5. SAT (combined) scores of college bound seniors in high school has the normal distribution with a mean of 1050 and a standard deviation of 150.
1. Sketch the Normal density curve that matches the information above.
2. What interval contains the middle 68% of the distribution of SAT scores of a college-bound senior?
(900, 1200)
3. What percent of students score between 900 and 1500?
Empirical Rule: 83.85
Calculator: 0.83999
4. Find the value such that 16% of all seniors have SAT scores below it.
Empirical Rule: 900
Calculator: 900.83
5. What is the 97.5th percentile of this distribution?
Empirical Rule: 1350
Calculator: 1343.99
6. The angiogram is a standard diagnostic test used in clinical medicine to detect strokes in patients. This test has some risks for the patient, and several noninvasive techniques have been developed that are hoped to be as effective as the angiogram. One such method utilizes the measurement of cerebral blood flow (CBF) in the brain, since stroke patients tend to have lower levels of CBF than normal. Among healthy people, CBF is normally distributed with a mean of 75 and a standard deviation of 17. Patients are classified as being at risk for stroke if their CBF is below 40. What proportion of normal patients will be classified as being at risk for stroke? 0.0198
7. Maple tree diameters in a forest area are normally distributed with mean 10 inches and standard deviation 2.2 inches. Find the proportion of trees having a diameter greater than 15 inches.
0.0115
8. Our subjects are 35-44-year-old males whose blood pressures are normally distributed with N(80, 12). A borderline hypertensive is defined as a person whose diastolic blood pressure is between 90 and 95 mm Hg.
a. What proportion of subjects are borderline hypertensive?
0.0967
b. A hypertensive is a person whose diastolic blood pressure is above 95 mm Hg. What proportion of subjects are hypertensive?
0.1056
9. Glaucoma is a disease of the eye that is manifested by high intraocular pressure. The distribution of intraocular pressure in the general population is approximately normal with mean 16 mm Hg and standard deviation 3.2 mm Hg. If the normal range for intraocular pressure is between 10 and 22 mm Hg, than what proportion of the general population would fall within this range?
0.9392
10. White blood cell (WBC) count per cubic millimeter of whole blood has approximately the N(7500, 1750) distribution. The lowest 2% of all WBC counts are defined to be probable risks. How low must one's WBC count be to fall in the at-risk group?
3905.94
11. The resting heart rate for healthy adult horses averages 46 beats per minute with a standard deviation of 8 beats per minute. A horse whose resting heart rate is in the upper 10% of the distribution may have a secondary infection or illness that needs to be treated. How fast must a healthy horse's heart be beating to fall into this at-risk group?
56.25
12. The Graduate Record Examination (GRE) is widely used to help predict the performance of applicants to graduate school. The range of possible scores on a GRE is 200 to 900. The math department at a university finds that the scores of its applicants on the verbal portion of the GRE (VGRE) are approximately normal with mean m = 612 and standard deviation s = 103. To be accepted into a graduate program at this university, a student must score in the top 25% of the GRE. What score must a student get to be accepted?
681.47
13. Jenny is 5’10” tall and is worried about her height. The heights of girls in the school are approximately normally distributed with a mean of 5’5” and a standard deviation of 2.6”. What is the percentile rank of Jenny’s height?
.9728 or the 97th percentile
14. A set of 5,000 scores on a college readiness exam are known to be approximately normally distributed with mean 72 and standard deviation 6. To the nearest integer value, how many scores are there between 63 and 75?
0.6247(5000) = 3123.5
15. One of the values in a normal distribution is 43 and its z-score is 1.65. If the mean of the distribution is 40, what is the standard deviation of the distribution?
Sx = 1.82
16. A group of 15 students were identified as needing supplemental help in basic arithmetic skills. Two of the students were put through a pilot program and achieved scores of 84 and 89 on a test of basic skills after the program was finished. The other 13 students received scores of 66, 82, 76, 79, 72, 98, 75, 80, 76, 55, 77, 68, 69. Find the z-score for the students in the pilot program and comment on the success of the program.
Mean: 76.4, Sx = 10.17
Z1 = 0.747
Z2 = 1.239
Since both z-scores are positive, it appears that the pilot program is successful.
17. The cumulative relative frequency graph below shows the distribution of lengths (in centimeters) of fingerlings at a fish hatchery. Find the interquartile range for this distribution.
[pic]
IQR = 6.6 – 5.4 = 1.2
18. The distribution of the heights of students in a large class is roughly Normal. Moreover, the average height is 68 inches, and approximately 95% of the heights are between 62 and 74 inches. What is the standard deviation of the height distribution?
Sx = 3
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