Quiz #7 (A) contains 6 questions about probability and statistics concepts. Question 1 asks to define a random variable with an example. Question 2 asks to find the average family size and variance based on a given probability distribution for family size. Question 3 asks to find the expected value and variance of a random variable with a given probability density function. Question 4 asks to find the probability that 3 out of 5 randomly selected patients will recover given survival rate data. Question 5 asks to find the probability that a sample of 200 items will contain exactly 4 defective items given a known defect rate. Question 6 asks to find probabilities related to the standard normal distribution.

1. Quiz # 7 (A)
1. Explain the concept of random variable with an example.
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) 0 0.3 0.2 0 0.1 0.4
A) Find the average family size E(X).
B) Also find V(X).
3. f(x)=x5 ; 0<x<1
A) Find E(X).
B) Also find V(X).
4. Hospital records show that of patients suffering from a certain
disease, 55% die of it. What is the probability that of 5 randomly
selected patients, 3 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 200
electric motors will contain exactly 4 defective motors?
6. Find the following probabilities:
(a) P(Z > 1.11)
(b) (c) P(1.14 < Z < 2.05)

2. Md. Mortuza Ahmmed