i) The average number of acres of land cultivated with food grains is normally distributed with mean 4,300 acres per year, and standard deviation of 750 acres. What is the probability that between...

i) The average number of acres of land cultivated with food grains is normally distributed

with mean 4,300 acres per year, and standard deviation of 750 acres. What is the

probability that between 2,500 and 4,200 acres will be cultivated in any given year?
What number of cultivated acres corresponds to the 38th percentile?
ii) The random variable X has a range of {0, 1, 2} and the random variable Y has a range

of {1, 2}. The joint distribution of X and Y is given by the following table:

y→
x↓
1 2
0 0.2 0.1
1 0 0.2
2 0.3 0.2
a) Find the marginal distribution of X and Y
b) What is the conditional distribution of X given Y=2.
c) Compute Cov (X,Y)
d) Are X and Y independent?
iii) For short distance flights, AVX airways provides three different choices on its snack

menu—mixed nuts, potato chips, and cookies. The airline observes in the past that each

snack is equally likely to be chosen. If there are 150 passengers on a particular flight,

what is the approximate probability that

a) At least 60 will choose mixed nuts?

b) Fewer than 60 will choose mixed nuts?

iv)Ratio of the probability of 3 successes in 5 independent trials to the probability of 2

successes in 5 independent trials is ¼. What is the probability of 4 successes in 6

independent trials?