Statistics and Probability Answers

Let X be a random variable that denotes the number of passengers in a train station for a given hour. What are the possible values of X?

Growth factors for the population of Chattanooga in the past two years have been 8 and 12. Find the value of the geometric mean.

In a binomial distribution the probability of getting zero or more number of successes is equal to

a. 0

b. the probability of getting zero success

c. the probability of getting successes in all the trials

d. 1 minus the probability of getting successes in all the trials

e. 1

Which of the following is true if the coefficient of correlation between two variables X and Y is zero?

a) covariance is zero

b) covariance is positive

c) covariance is negative

d) variance of X is zero

e) variance of Y is zero

Happening of an event precludes the happening of another. These events are

a) independent events

b) joint events

c) mutually exclusive events

d) both A and C

e) both b and c

It was to be determined whether there was any relation between type of music listened to by 30 year old people and the geographic location of their residence. From the table below, you are requested to test 1% level of significance whether music preference is independent of geographic location.

Region Rock music Romantic music country music classical music

NORTH 150 52 8 20

south 147 49 56 9

west 163 29 6 11

Data from department of agriculture in a country show that average size of the farms has increased since 1975. In 1975 the mean size of the farm was 471 acres. an agribusiness researcher believes that average size of the farm has increased. To test this a random sample of 23 farms across the country was taken. The sample mean was found to be 498.78 acres with a standard deviation of 46.94. using 5% level of significance, test whether agribusiness researcher's belief is true or not?

The environmental protection agency publishes figures on solid waste generation in a city. one of the year, the average number of waste generated per person per day was 3.59 pounds. Suppose the daily amount of waste generated per person is normally distributed with a standard deviation of 1.04 pounds. What is the amount of waste generated per person by 67.72% of the people in the city?

Suppose that six coins are tossed simultaneously 640 times and the following frequency distribution in observed

Number of heads 0,1,2,3,4,5,6

Observed frequency 13,70,137,210,145,56,9

Test the null hypothesis that the coins are well balanced with Ω0.01

THE DATA DEPICTED BELOW IS FROM S. LTD. WHERE 300 EMPLOYEES WITH VARIOUS CATEGORIES OF PROFESSION ARE ON ROLLS.

Position Male female

Managerial 16 6

Professional 50 30

Technical 100 36

Clerical 18 44

Find the probability that:

1) A randomly selected employee is a female or a professional worker

2) A randomly selected employee is a female

3) A randomly selected employee who is found to hold a managerial position is a female

4) A randomly selected female employee having clerical position

5) A randomly selected employee given that he is a male is from technical position.