The document is a midterm examination for a statistics course consisting of 6 questions testing concepts like probability, distributions, correlation, and hypothesis testing. The exam covers finding probabilities of coin tosses, determining values and measures from a probability distribution of family sizes, calculating the probability of patient recovery outcomes, and interpreting correlation coefficients. It is worth a total of 100 marks and must be completed within 50 minutes.

1. INTERNATIONAL UNIVERSITY OF BUSINESS AGRICULTURE AND TECHNOLOGY
Midterm examination STA 240
Full marks: 100 (80+20) Time: 50 minutes
1. Two coins are tossed; find the probability that
a) At most one tail is obtained.
b) At least one head is obtained.
2. The number of persons X, in a family chosen at random has the following probability
distribution:
X 1 2 3 4
P(X) 0.25 0.25 m 0.25
A) Find the value of m.
B) Find the average family size E (X).
C) Also find V(X).
3. 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?
4. 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 5
defective motors?
5. Interpret the following results :
a) r = 0.79 b) r = 0.65 c) r = 0.34 d) r = 0.18
6. A jar contains 3 red marbles, 7 green marbles and 5 white marbles. If a marble is drawn
from the jar at random, what is the probability that
a) The marble is white?
b) The marble is either white or red?
Md. Mortuza Ahmmed

2. Submit quiz 8 for the remaining 20 marks within tomorrow