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If the uric acid values in normal adult males are approximately normally distributed with mean 4.7 mgs and standard deviation 1mg find the probability that a sample of size 9 will yield a mean.
A health officer is trying to study the malaria situation of Ethiopia. From the records of
seasonal blood survey (SBS) results he came to understand that the proportion of people
having malaria in Ethiopia was 3.8% in 1978 (Eth. Cal). The size of the sample
considered was 15000. He also realised that during the year that followed (1979), blood
samples were taken from 10,000 randomly selected persons. The result of the 1979
seasonal blood survey showed that 200 persons were positive for malaria. Help the
health officer in testing the hypothesis that the malaria situation of 1979 did not show
any significant difference from that of 1978 (take the level of significance, α =.01).
Each of two groups consists of 100 patients who have leukaemia. A new drug is given to
the first group but not to the second (the control group). It is found that in the first
group 60 people have remission for 2 years; but only 40 in the second group. Find 95%
CI.
following statement is true and which are false? Give reasons for your answers, in the form of a short proof or a counter example.
Every continuous function is differentiable
Let R={(1,2),(1,4),(2,1),(2,4),(3,2),(3,4)}
R={(1,2),(1,4),(2,1),(2,4),(3,2),(3,4)}
is a relation on set A={1,2,3,4}
A={1,2,3,4}
Suppose a Rn b
means that there is a path of length n from a
to b
Which of the elements are R3?
An experiment was conducted to study the effect of pesticides on plant species that are exposed to them. Different dosages of pesticides were administered to 4 groups of 4 mice. The 16 mice were females of similar age and condition. One group received no pesticides. The response Y was measure of brain activity. It was postulated that brain activity (Y in moles/liters per minute) would decrease with an increase in dosage (X in mg/kg body weight)
Dose (X)
0.0, 0.0, 0.0, 0.0, 2.5, 2.5, 2.5, 2.5
Activity (Y)
10.6, 10.4, 10.8, 11.0, 11.0, 11.3, 10.3, 9.9
Dose (X)
5.0, 5.0, 5.0, 5.0, 7.5, 7.5, 7.5, 7.5
Activity (Y)
9.5, 9.2, 9.7, 8.6, 8.2, 8.0, 8.4, 7.8
a) test if there is a significant linear relationship between the dose and the brain activity by constructing an analysis of variance table for the above data.
b) compute r and interpret the result
S. Mr. X is known to hit the target in 4 out of 5 shots, where as Mr. Y is known to hit the target in 3 out of 5 shots. Find the probability that both will hit the Target
S. The efficiency rating of 155 faculty members of a certain college was taken and is shown below
Classes f
73-75 2
76-78 6
79-81 12
82-84 16
85-87 18
88-90 39
91-93 36
94-96 21
97-99 5
Determine the value of
1. P36
2. D5
3. Q3
DM. Let a and b be two cardinal numbers. Modify Cantor’s definition of a < b to define a ≤ b. (Hint: Examine what happens if you drop condition (a) from Cantor’s definition of a < b.) 2. Prove that a ≤ a. 3. Prove that if a ≤ b and b ≤ c, then a ≤ c. 4. Do you think that a ≤ b and b ≤ a imply
a = b? Explain your reasoning. (Hint: This is not as trivial as it might look.)
Express 1/(cos θ − i sin θ) in the form of a + ib and hence prove that
cosθ+isinθ/ cos θ − i sinθ = cos2θ+isin2θ.
