Download EXERCISES

EXERCISES
SAMPLING DISTRIBUTION
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?
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%?
QUESTION 3
If the distribution of daily calorie intake in boys aged 23 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:
A) Greater than 144?
B) Less than 88?
C) Between 88 and 144?
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%
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:
EXERCISE
•
•
•
•
26 seconds or more
Between 24 and 27 seconds
26 seconds or less
Greater than 22 seconds
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?
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?
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 ?