Homework: Probability and Normal Distribution
Q1. What two scores would divide a normal distribution such that approximately 68% of the general population falls within them if the mean is 100 and the standard deviation is 15?
a. 80 to 120
b. 85 to 115
c. 90 to 110
d. 75 to 125
Q2. If you want to calculate a z score for a test where your raw score was 24, what other information must you know?
a. Shape of the distribution
b. Mean, median, and mode
c. Mean and standard deviation
d. Standard deviation only
Q3. To calculate a z-score, you:
a. subtract the mean from the raw score, and divide this difference by the standard deviation
b. subtract the mean from the raw score, and divide this difference by the variance
c. subtract the raw score from the mean, and divide this difference by the standard deviation
d. subtract the raw score from the mean, and divide this difference by the variance
Q4. What is the z score for a raw score of 85 where the group mean is 75 and the standard deviation is 5?
a. -2.0
b. 2.5
c. 2.0
d. -2.5
Q5. Calculate s to be -6. From this, you know that
a. s2 = -36
b. s2 = 36
c. s = 6
d. Using the variance formula, -6 is not possible.
Q6. A school nurse was asked to give two training programs for school children on drug abuse awareness: One will be for children with no drug knowledge and another for children who already have a moderate amount of knowledge. She asks the school district to divide the children into more knowledgeable and less knowledgeable groups prior to her arrival, so that she can instruct them separately.
She gives the school district a drug knowledge quiz to administer so that they can use the scores as the basis of separating the children. Because of the nature of the training exercises, she would like the two groups to be the same size.
What measure of central tendency should school district administrators apply to the drug pretest scores in order to break the class into more knowledgeable and less knowledgeable groups? Why?
Q7. F or the following situations, specify the independent and dependent variables AND the levels of measurement for EACH variable.
a. A nurse wishes to determine the effect of reminiscence therapy on depression survey scores (Likert type scale) of a group of geriatric patients in a long term care facility.
b. In a study of the effect of smoking cessation treatment in an ambulatory care settingand the number of cigarettes smoked per day by each participant.
c. In a study of the effect of tai chi sessions on lower back pain, an investigator obtained the pain score of the participating patients after each tai chi session.
d. A nurse researcher wanted to determine the relationship between years of RN experience, specialty certification and patient deaths in a hospital setting.
Q8. Here are the diastolic blood pressures of 10 patients prior to a diet and medication regimen.
120, 116, 104, 102, 105, 112, 104, 111, 107, 100
Find the (a) range, (b) variance, and (c) standard deviation for the blood pressures. Show your work.
Q9. For a midterm nursing statistics exam, the mean score is 70 with a SD of 10.Student ratings on the exam are classified as follows.
2-3 standard deviations below the mean= very poor
1-2 standard deviations below the mean= poor
0-1standard deviations below the mean= average
0-1standard deviations above the mean = average
1-2 standard deviations above the mean= good
2-3 standard deviations above the mean= excellent
Classify the following students with regard to their score (poor/average/good/excellent)
a. 95
b. 65
c. 72
d. 52
e. 82
Q10. Using the z distribution table, find the proportion of the total area for the following, draw a picture of each, and shade in the target area.
a. Between a z score of 0.00 and a z score of 1.64
b. Above a z score of 1.64
c. Between a z score of 0.00 and a score of -1 .00.
d. Below a z score of -1 .64.
e. Below a z score of 0.00.
f. Between a z score of -1.00 and a z score of 1.00.
g. Between a z score of -2.00 and a z score of -1 .00.