problem 1:

a) Out of 800 families with 5 children each, how many would you expect to have:

i) 3 boys
ii) 5 girls
iii) Either 2 or 3 boys

b) Suppose that 50% of all engineering students are good in mathematics. Find out the probabilities that among 18 engineering students:

i) Exactly 10
ii) At least 10
iii) Utmost 8 are good in mathematics

problem 2:

a) The marks obtained in Mathematics by 1000 students are normally distributed with mean 78% and standard deviation 11%. Find out:

i) How many students got marks above 90%?
ii) What was the highest mark obtained by the lowest 10% of the students? Within this limits did the middle of 90% of the students lie.

b) In 256 sets of 12 tosses of coin, in how many cases one can expect 8 heads and 4 tails.

problem 3: A Population comprises of 4, 8, 12, 16, 20. Consider all samples of size three which can be drawn without replacement from this population. Determine:

a) Mean of the population.
b) Standard deviation of the population.
c) Mean of the sampling distribution of means.
d) Standard deviation of the sampling distribution of means.
e) Compare the results of (a), (c) and (b), (d). Find out correction factor of the population.

problem 4:

a) A random sample of size 100 is taken from an infinite population having the mean 76 and the variance 256. Determine the probability that the sample mean will be between 75 & 78.

b) A sample of size 400 is taken from a population whose standard deviation is 16. Find out the standard error and probable error.