**[OBJECTIVE]**

**Subject:** Probability and Probability Distributions

**Time Allowed:** 15 Minutes

**Max Marks:** 10

**NOTE:** Attempt this Paper on this Question Sheet only. Please encircle the correct option. Division of marks is given in front of each question. This Paper will be collected back after expiry of time limit mentioned above.

__Part-I Answer the following Questions, cutting and overwriting are not allowed. (10)__

What is probability of drawing two clubs from a well shuffled pack of 52 cards?

a) 13/51 b) 1/17

c) 1/26 d) 13/17

When two coins are tossed simultaneously, what are the chances of getting at least one tail?

a) 3/4 b) 1/5

c) 4/5 d) 1/4

If value of x for normal distribution is 35, mean of normal distribution is 65 and standard deviation is 25 then standardized random variable is

a) -1.5 b) -1.2

c) -1.7 d) -4

Probability of second event in situation if first event has been occurred is classified as

a) series probability b) conditional probability

c) joint probability d) dependent probability

In which of the following sampling methods are the “n” individuals subdivided into separate subpopulations with a common characteristic?

a) Stratified sample b) Cluster sample

c) Systematic sample d) None of the above.

Obtaining too many males in your sample would be an example of which of the following types of survey errors?

a) Measurement error b) Sampling error

c) Coverage error d) Nonresponse error

In probability theories, events which can never occur together are classified as

a) collectively exclusive events b) mutually exhaustive events

c) mutually exclusive events d) collectively exhaustive events

In normal distribution

a) Mean = Median = Mode b) Mean < Median < Mode

c) Mean > Median > Mode d) Mean ≠ Median ≠ Mode

Which of the following sampling methods is a probability sample?

a) Chunk sample b) Simple random sample

c) Quota sample d) Judgment sample

According to the central limit theorem, the sampling distribution of the mean can be approximated by the normal distribution:

a) As the number of samples gets “large enough.”

b) As the size of the population standard deviation increases.

c) As the sample size (number of observations) gets “large enough.”

d) As the size of the sample standard deviation decreases.

**[SUBJECTIVE]**

**Subject:** Probability and Probability Distributions

**Time Allowed:** 2 Hours 45 Minutes

**Max Marks:** 50

**NOTE:** ATTEMPT THIS (SUBJECTIVE) ON SEPARATE ANSWER SHEET PROVIDED

__Part-II Give Short Answers, Each question carries equal marks. (20)__

**Q#**1: Differentiate between discrete random variables and continuous random variables.

**Q#**2: Differentiate between Mutually Exclusive Events and Collectively Exhaustive Events.

**Q#**3: Differentiate between simple random sampling and stratified sampling.

**Q#**4: Differentiate between type I and type II error.

**Q#**5: Explain the central limit theorem.

__Part-III Give Long Answers, Each question carries equal marks. (30)__

**Q#**3: Thirty random observations are taken from each of the following distributions and the sample mean calculated. Find, in each case, the probability that the sample mean exceeds 5.

**a)**X is the number of telephone calls made in an evening to a counseling service, where X~ Po**b)**X is the number of heads obtained when an unbiased coin is tossed nine times.

**Q#**4: **a)** The masses, in grams, of thirteen ball bearings taken at random from a batch had a mean of 24.9231 and a variance of 5.74. Calculate a 95% confidence interval for the mean mass of population supposed normal, from which these masses are drawn.

**b)**The amount of nicotine, in milligrams, in a cigarette of a certain brand is normally distributed with mean j: and standard deviation 2.5. A random sample of 10 cigarettes yielded a mean nicotine value of 18.4, Test the null hypothesis p = 17.8 against the alternative hypothesis 1 # 17.8 at the 10 % significance level.

**Q#**5: **a)** A ball is drawn at random from a box containing 6 red balls, 4 white balls and $ blue balls. Determine “the probability that the ball drawn is

- Red
- White

**iii.** Blue

- Not red
- Red or white
- b) What is probability that a card chosen at random from a standard deck of cards will be either a Jack or a Diamond?