1. SAMPLING DISTRIBUTION
EXERCISES
SAMPLING DISTRIBUTION

2. QUESTION 1
If the uric acid values in normal adults males are approximately normally distributed with a mean =5.7 mg/dl, and a standard deviation = 1 mg/dl . Find the probability that a sample of 9 will yield a mean of:
a) Greater than 6?
b) Between 5 and 6?
c) Less than 5.2?

3. QUESTION 2
If in a population of adults 15% are on some sort of diet. What is the probability that a random sample of 100 from this population will yield a proportion who are on diet:
A) Greater than or equal 20%?
B) Between 10-20%?
C) Less than 12%?

4. QUESTION 3
If the distribution of daily calorie intake in boys aged 2-3 years is normally distributed with a mean of 1403, and a standard deviation of 205; and that of boys aged 1-2 years is also normally distributed with a mean of 1287 and a standard deviation of 198. If independent samples of 25 boys aged 2-3 years, and 27 boys aged 1-2 years are obtained , what is the probability that the difference between the sample means is:
Greater than 144?
Less than 88?
Between 88 and 144?

5. QUESTION 4
If in a population A, 20% of school children posses sickle cell trait, while among population B this trait is present in 12% of school children. If independent samples of size 150 from population A, and 200 from population B: what is the probability that the difference in proportions of the trait between the two samples is:
A) <6%
B) >10%
C) between 6-10%

6. EXERCISE
It has been found that after a period of training , the mean time required for certain handicapped persons to perform a particular task is 25 seconds, with a standard deviation of 5 seconds.
Assuming a normal distribution of times, find the probability that a sample of 25 individuals will yield a mean of:

7. EXERCISE 26 seconds or more Between 24 and 27 seconds
26 seconds or less
Greater than 22 seconds

8. EXERCISE
In population A , the average annual family expenditure on general health is 380 $, with a variance of 2899 $2. In population B the comparative figures were 380 $, and 3250 $2.
A random sample of 40 families from population A , and 35 families from population B, showed average annual expenditure on health of 346 $ and 300 $ ,respectively.
Find the probability of such a difference or higher?

9. EXERCISE
In a certain city , it is felt that 205 of household had at least one member who is suffering from ill health due to air pollution. A random sample of 150 household yielded a prevalence of 27%. What is the probability of having such a prevalence or higher?

10. EXERCISE
A psychiatric social worker believes that in both community a and community b , the proportion of adolescents suffering from some mental or emotional problem is 20%.
In a sample of 150 adolescents from community A, 15 had mental or emotional problem. In a sample of 100 from community B, the number was 16.
What is the probability of observing such a difference or higher ?