The document contains 6 questions regarding probability distributions and statistics. Question 1 asks about the properties of Poisson and normal distributions. Question 2 provides a probability distribution for family size and asks to calculate the expected value and variance. Question 3 gives a uniform distribution and asks for expected value and variance. Question 4 asks for the probability of recovering from a disease. Question 5 asks for the probability of defective motors in a sample. Question 6 asks for probabilities related to the standard normal distribution.

1. Quiz # 7 (D)
1. Write down the applications of Poisson distribution and properties of
normal distribution.
2. The number of persons X, in a family chosen at random has the
following probability distribution:
X 1 2 3 4 5 6
P(X) 1/6 1/6 1/6 1/6 1/6 1/6
A) Find the average family size E (X ).
B) Also find V(X).
3. f(x)=x ; 0<x<1
A) Find E (X ).
B) Also find V(X).
4. Hospital records show that of patients suffering from a certain
disease, 75% die of it. What is the probability that of 6 randomly
selected patients, 4 will recover?
5. A company makes electric motors. The probability an electric motor
is defective is 0.01. What is the probability that a sample of 300
electric motors will contain exactly 5 defective motors?
6. Find the following probabilities:
(a) P (Z > 1.06)
(b) (c) P (1.06 < Z < 2.14)

2. Md. Mortuza Ahmmed