This document appears to be a quiz for a statistics exam with 7 questions covering various statistical topics: 1. Properties of the Poisson distribution and normal distribution. 2. Definition of a random variable with an example. 3. Finding values for a probability distribution of family sizes including the value of m, the average family size, and the variance. 4. Calculating the expected value and variance for a given probability density function. 5. Finding the probability that 5 out of 10 randomly selected patients will recover from a disease where the probability of death is 25%. 6. Finding the probability that a sample of 500 electric motors will contain exactly 10 defective motors, given a 5% probability

1. INTERNATIONAL UNIVERSITY OF BUSINESS AGRICULTURE AND TECHNOLOGY
Quiz examination
STA 240 Set: Z
Full marks: 100 Time: 50 minutes
1. Write down the applications of Poisson distribution and properties of normal distribution.
2. What is random variable? Explain with an example.
3. The number of persons X, in a family chosen at random has the following probability
distribution:
X 1 2 3 4 5
P(X) 0.1 0.2 m 0.1 0.2
A) Find the value of m.
B) Find the average family size E (X).
C) Also find V(X).
4. p(x)=7x10 ; 1<x<2
A) Find E (X).
B) Also find V(X).
5. Hospital records show that of patients suffering from a certain disease, 25% die of it.
What is the probability that of 10 randomly selected patients, 5 will recover?
6. A company makes electric motors. The probability an electric motor is defective is 0.05.
What is the probability that a sample of 500 electric motors will contain exactly 10
defective motors?
7. Find the following probabilities:
(a) P (Z > 1.06)
(b) (c) P (1.01 < Z < 2.04)

2. Md. Mortuza Ahmmed