Learn Probability And Statistics

Hey , could you please give here sample questions on Probability And Statistics for preparation of a bank exam ?

[Shaleen]

As you want I am here giving you sample questions on Probability And Statistics for preparation of a bank exam.

Sample questions:

1)The probability of rain tomorrow is .30, and the probability of all members of ECN 215 being present in class is .6 (let us say). What is the probability of both these events occurring?

2)For each of the following pairs, state whether you think the events are statistically independent or not. Explain briefly.
Disposable income and consumption in the US.
Consumption in the US and GNP in Britain.
Rainfall and the rate of inflation.
Rainfall and the price of corn.
An individual's shoe size and her height.
An individual's shoe size and her income.


3)Suppose that Wake Forest students have a mean height of 68 inches, with a standard deviation of 3 inches. If heights are normally distributed, what is the probability that a randomly-selected Wake Student is between 63 and 73 inches tall?

4)(continuation of question 3) Rachel, who is not aware of the above information, intends to draw a random sample of 50 Wake students in order to estimate the population mean height. What is the probability that the sample mean height she obtains lies between 63 and 73 inches?

5)(continuation of question 3) Can you think of any reason why the heights of Wake Forest students might not follow the normal distribution?

6)You are trying to estimate the average houshold income in Forsyth County. You randomly sample 200 households, and come up with the following sample statistics: mean = $28000, standard deviation = $5000. Draw up the 95 per cent confidence interval for your estimate of the population mean income. Give a brief interpretation of your answer.

7)A researcher is experimenting with several regression equations. Unknown to him, all of his formulations are in fact worthless, but nonetheless there is a 5 per cent chance that each regression will--by the luck of the draw--appear to come up with `significant' results. Call such an event a `success'. If the researcher tries 10 equations, what is the probability that he has exactly one success? What is the probability of at least one success?


8)Quality control requires that Brito light bulbs have an average life of 1000 hours, with a standard deviation of no more than 20 hours. Each month, a sample of 50 bulbs is tested to see whether current production is meeting the standard. If a statistically significant deviation from 1000 hours mean life is found, the production process must be inspected for faults. In this context, `statistically significant' is taken to mean that the probability that the observed deviation of the sample mean from 1000 is due to chance alone is 10 per cent or less. This month the sample mean life turns out to be 996 hours. What is the probability that this deviation from 1000 is just due to sampling error? Does this sample call for inspection of the production process?

9)In a group of 40 people, 10 are healthy and every person the of the remaining 30 has either high blood pressure, a high level of cholesterol or both. If 15 have high blood pressure and 25 have high level of cholesterol,
a) how many people have high blood pressure and a high level of cholesterol?


10)If a person is selected randomly from this group, what is the probability that he/she

b) has high blood pressure (event A)?

c) has high level of cholesterol(event B)?

d) has high blood pressure and high level of cholesterol (event A and B)?

e) has either high blood pressure or high level of cholesterol (event A or B)?

f) Use the above to check the probability formula: P(A or B) = P(A) + P(B) - P(A and B).


11)A committee of 5 people is to be formed randomly from a group of 10 women and 6 men. Find the probability that the committee has
a) 3 women and 2 men.
a) 4 women and 1 men.
b) 5 women.
c) at least 3 women.


12)In a school, 60% of pupils have access to the internet at home. A group of 8 students is chosen at random. Find the probability that
a) exactly 5 have access to the internet.
b) at least 6 students have access to the internet.


13)The grades of a group of 1000 students in an exam are normally distributed with a mean of 70 and a standard deviation of 10. A student from this group is selected randomly.
a) Find the probability that his/her grade is greater than 80.
b) Find the probability that his/her grade is less than 50.
c) Find the probability that his/her grade is between 50 and 80.
d) Approximately, how many students have grades greater than 80?