STAT– 835 : PROBABILITY AND STATISTICS Fall 2015

Assignment – 1 Due Date: 22 Oct 2015 Max Marks: 75

Question-1 (15)

With reference to population and sampling;

a. Assume and define a population and define the data required for a particular “parameter” of

that population.

b. Select a “sampling method” for the assumed population with reasons/justification.

c. Search and quote/explain an example/case of sampling method selection for population

parameter determination, attach the source document (use some book or internet source)

Question-2 (30)

Assume any data comprising of at least 25 values including at least two outliers (at least one mild and

extreme each).

a. Describe the data as discrete or continuous.

b. Using SPSS, answer following:

Find descriptive statistics of the sample data.

Draw Histogram and describe its basic properties including shape, skewness, data gaps (if

any), central tendency, etc.

Draw Boxplot and give its five point summary and define outliers of the data.

Draw stem and leaf plot and describe its important features.

Determine the values which are 1.5 times the standard deviation, below and above the mean

of the data.

Determine how many standard deviations are the outliers away from the mean.

Determine following percentiles of the data: 25th

,50th

,75th

and 85th

.

Question-3 (20)

A survey report reveals that generally 6 out of 20 car drivers wear seat belt and 12 out of 30 cars have

ABS brakes. Probability that car has ABS brakes and its driver is wearing seat belt is 20%.

What is the probability that:

a. A randomly selected car has at least ABS brakes. Draw the corresponding van diagram and

write appropriate probability equation.

b. A randomly selected car has ABS brakes but its driver is not wearing seat belt. Draw the

corresponding van diagram and write appropriate probability equation.

c. A randomly selected car driver is wearing seat belt but no ABS brakes in his car. Draw the

corresponding van diagram and write appropriate probability equation.

d. Neither a randomly selected car driver is wearing seat belt nor there are ABS brakes in his car.

Draw the corresponding van diagram and write appropriate probability equation.

Question-4 (10)

Give a detailed example of use permutation and combination (each) counting technique in order to find

the probability of an event (other than the examples solved in class notes). Quote the reference.