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ˆ Homework assignment must be done cleanly in A4 size papers, must be stapled (if extends more than one sheet
of paper).
ˆ Solutions and answers must be written in complete sentences
ˆ Hand writing should be readable.
ˆ Maximum mark 25%
ˆ No late homework will be accepted.
1. The birth weights(Kilogram) of 30 children were recorded as follows
2.0,
4.0,
3.1,
2.1,
2.3,
3.0,
2.3,
3.5,
2.6,
3.0,
4.2,
2.8,
3.1,
3.7,
2.9,
2.7,
3.2,
3.5,
2.8,
2.7,
4.1,
3.5,
2.5,
3.9,
3.1,
2.7,
2.8,
3.7,
3.8,
2.2
(a) Construct grouped frequency distribution.
(b) Draw frequency polygon , histogram and ogive curve.
(c) Calculate Arithmetic mean and standard deviation.
(d) Calculate median value and mode value.
2. A total of 20 patients admitted to a hospital are tested for levels of blood sugar, (mg/dl) and the results were
summarized below
Class-Limit
A-B
C - 17
E-F
G-H
30 - I
K-L
Class-Boundary
Number of people
LCF
7
4
MCF
20
18
16
Class Mark
18
Then,
(a) Complete the above table
(b) Calculate Mean and Median
(c) Draw histogram, a frequency polygon , and a less than ogive for the above table.
3. In an insurance company study of the causes of 1000 deaths, the following data were obtained
Cause of death
Heart disease
Cancer
Stroke
Accidents
Other
No of Deaths
432
217
93
34
224
Construct a pie chart to represent the data
4. The mean and standard deviation of the distribution of the weights of a group of 100 patients are found to be 40
kgs and 10 kgs respectively. If at the time of calculation two observations were wrongly taken as 30 kg and 70 kg
in place of 3 kg and 27 kg respectively, find the correct standard deviation.
5. The median and mode of the patient waiting time at hospital to visit a doctor are 33.5 minutes and 34 minutes
respectively.
Minute
0-10
10-20
20-30
30-40
40-50
50-60
60-70
Total
Frequency
4
16
F1
F2
F3
6
4
230
Determine the missing frequencies, and compute the arithmetic mean.
6. A hospital collected data on the age group of each of 120 people that were treated as outpatients on a particular
day. the results are summarized below
Age group
Number of people
pre-school
school
60 and above
others
18
24
35
43
Draw a appropriate bar chart to illustrate these results
7. A student received an A in Basic writing skills (3 credits), a C in Human Physiology (3 credits), a B in Biochemistry
(4 credits), and a D in Medical Microbiology (2 credits). Assuming A=4 grade points, B=3 grade points, C=2
grade points, D=1 grade point, and F=0 grade points, find the student’s grade point average.
8. Gadise obtained results of 63 in Biostatistics and 58 in Biochemistry. For Biostatistics the class mean was
58 and the standard deviation 3.4, and for Biochemistry the class mean was 55 and the standard deviation 2.3.
Compared to the rest of the class did Gadise do better in Biostatistics or Biochemistry?
9. A dietitian is interested in comparing the sodium content of real cheese with the sodium content of a cheese
substitute. The data for two random samples are shown.
Real cheese
310
220
420
240
45
180
Cheese Substitute
40
90
270
130
180
260
250
340
290
310
Compute coefficient of variation and interpret it.
10. The combined mean of 50 students who passed and failed in Biostatistics is 51.6. If the number of students who
passed is 40 and its mean is 59.25. Find out the mean marks of the students who failed?
11. A study was conducted to determine the effectiveness of varying amounts of vitamin C in reducing the number of
common colds. A survey of 450 people provided the following information:
Daily amount of vitamin C taken
None
500 mg
1000 mg
No colds
57
26
17
At least
one cold
223
84
43
Is there evidence of a relationship between catching a cold and taking vitamin C?
12. Ten persons came into contact with a person infected with tuberculosis. The probability of being infected after
contacting a person with tuberculosis is 0.1.
(a) What is the probability that nobody is infected?
(b) What is the probability that at least 2 persons are infected?
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(c) What is the expected number of infected persons?
13. A general practitioner doctor is interested in knowing how many years her patients stay with her. Let X = the
number of years a patient will stay with the doctor. Over the years, she has established the following probability
distribution:
x
1
2
3
4
5
6
7
P (X = x)
0.1
0.2
0.1
K
2K
0.2
0.1
(a) Find the value K, E (x) and Var (x)
14. Assume the cholesterol levels of adult American women can be described by a Normal model with a mean of 188
mg/dL and a standard deviation of 24.
(a) What percent of adult women do you expect to have cholesterol levels over 200 mg/dL?
(b) What percent of adult women do you expect to have cholesterol levels between 150 and 170 mg/dL?
15. A box contains 24 bottles of pills , 4 of which are defective. If 4 are sold at random, find thefollowing probabilities.
(a) Exactly 2 are defective.
(b) None is defective.
(c) All are defective.
(d) At least 1 is defective.
16. A drug company is testing a new drug which is supposed to reduce blood pressure. From the six people who are
used as subjects, it is found that the average drop in blood pressure is 2.28 points, with a standard deviation of
.95 points.
(a) What is the 95% confidence interval for the mean change in pressure?
17. Several studies have shown that women with many children are less likely to get ovarian cancer. In a new study,
data are collected from 25 women ages 40-49 with ovarian cancer. The mean parity (number of children) of these
women is 1.8 with standard deviation 1.2. Suppose the mean number of children among women in the general
population in this age group is 2.5.
(a) What test can be used to test the hypothesis that women with ovarian cancer have fewer children than women
in the general population in the same age group?
(b) Perform the test
(c) Identify the critical region(s)
(d) What do you conclude from this study?
(e) What are the type I and type II errors for this question?
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