1.Identify Each Variable As Quantitative Or Qualitative

PJJ MTH 3003

SEMESTER 2 2016/2017

EXERCISES

1.Identify each variable as quantitative or qualitative:

(a) Number of students in first-grade classroom

(b) Amount of time it takes to assemble a simple puzzle

(d) Ethnic origin a of candidate for public office

(e) The color of M&M’s candy

2.Identify the following quantitative variables as discrete or continuous

(a) Population in a particular area of United States

(b) Time to complete a sociology exam

(d) Time required to complete a questionnaire

(e) Number of defective light bulbs in a package containing four bulbs

3.Classify thefollowing randomvariables as discrete or continuous

(a)The numberof female employees working for a company

(b)The amountof caffeine in a cup of coffee

(c)The time spent by a lawyer with aclient

(d)The numberofphone calls received at a police station on a day

(e)The price ofa football game ticket

4.A fair coin is rolled three times. Find the probability of observing

(a)exactlytwo tails.

(b)at least two tails.

5.How many ways we can select and arrange three letters from the word MUSIC?

6.Let A be an event of observing odd number and B as an event of observing number greater than 2 when a fair dice is tossed. Give the list of the simple events that are either in event A or B or both. Then, find its probability.

7.Hospital records show that a patients suffering from a chronic disease has 25% chance to recover.Let the random variableX represents the number ofpatients recoveredfrom thechronic disease. If 10 patientssuffering from a chronic disease is selected at random,

(a)find the possible values of X

(b)find the probability that exactly 5 patients will recover.

8.Given the following stem and leaf plot.

StemLeaf

0 |1 2

1 |2 3 7 9

2 |

3 |

4 |2 2 3 3 3 3 4

5 |1 1 3 3 8 9

Key: 1 | 2 means 12

Based on the above plot,

(a)Calculate first, second and third quartiles.

(b)Draw a box and whiskers plot and comment on your plot.

9.The followingtablelists theprobabilitydistribution of thenumber of customersvisiting aconveniencestore per 15 minutes.

/ 5 / 6 / 7 / 8 / 9 / 10
/ 0.12 / 0.2 / / 0.18 / 0.15 / 0.08

Based on the table,

(a)identify whether the given table is a discrete or continuous probability distribution

(b)find in terms of k

(c)findk(d)find (e)find

10.Let A and B be the events with , and . Compute .

11.In a food processing and packaging plant, there are, on the average, two packaging machine breakdowns per week. What is the mean of the number of machine breakdowns per week if the probability that no machine breakdowns per week is given by

12.A bowl contains sevenwhite and fourredcandies. A child selectsfivecandies at random without looking. What is the probability that there are threewhite and twored candies in the selection?

13.A random sample of size n is selected from a Binomial population with parameter p. What is

(a)themean of a sampling distribution of sample proportion,

(b)thestandard error of the

14.A random sample of size is selected from a Normal population with the mean and variance . Find

(a)themean of a sampling distribution of sample mean

(b)thestandard error of

15.The distribution of Calculus scores for first year Mathematics students is normally distributed with mean 115 and variance 256. Find the score which corresponds to z-scores of 1.96

16.Let X be a random variable representing the number of observing a tail when a fair coin is tossed three times.

(a)Construct the probability distribution function of X.

(b)Calculate the mean of X

(c)Calculate the standard deviation of X

17.The distribution of a score for 50 students in a calculus test had a minimum score value of 34, first quartile of 46, median of 52, third quartile of 74 and maximum score value of 85. Based on the given information,

(a)How many percent of students scored between 46 and 74 in the calculus test?

(b)What is the value of 25th percentile () for these data.