Statistics and Probability Answers

The Traffic Police department is concerned with the increase in Accidents on Shaheed-Millat Expressway.They are setting up a dedicated team to analyse the causes and propose a solution. Accidents can occur because of the sharp turns on road or unavailability of Pedistrian bridges. On the other hand, accidents can occur due to unsafe driving or human error. The observation was further breakdowned in


Shift Unsafe Road Conditions Human Error Morning 6% 28% Day 4% 12% Evening 5% 26% Night 3% 16% Table 5

If an accident report is selected randomly from the 170 reports, (a) what is the probability that the accident occurred on the Evening shift? (b) what is the probability that the accident occurred due to human error? (c) what is the probability that the accident occurred due to unsafe road conditions? (d) what is the probability that the accident occurred on either the evening or the night shift?

An University wishes to hire 4 faculty members for its newly established department. They have to select from a group of 8 Male and 7 Female applicants, all of whom are equally qualified to fill in the positions. If University selects 4 at random, what is the probability that ; a) All four will be Men b) All four will be Women c) Atleast one will be a Women d) Atleast one will be a Me

A firm purchases a microchip used in the manufacturing of LED screens from four different suppliers. TechZone supplies 30 percent of the total microchips, Advance Electronics 25 percent, PSP importers 18 percent, and TechParts inc. 32 percent. TechZone tends to have the best quality, as only 3 percent of its microchips arrive defective. Advance Electronics chips are 4 percent defective, PSP importers chips are 7 percent defective, and Parts Inc. are 6.5 percent defective. a) If a random chip is selected, what is the probability that the chip is defective b) A defective chip was discovered in the latest shipment. What is the probability that it came from TechZone supplies? c) A defective chip was discovered in the latest shipment. What is the probability that it came from Parts Inc.?

Pakistan Cricket Board in its central contract places its International players in four different categories, Category A, Category B, Category C and Emerging Players’ Category. Batsmen who are going to play in upcoming series fall into these four categories in the proportions 30 percent, 40 percent, 20 percent and 10 percent. The probability that a Category A player will get out without scoring a single run is 0.01, for Category B player its 0.04, for Category C player its 0.12 and the probability that an emerging player will get out on Zero is 0.06.

During a match after the fall of second wicket captain sent Muhammad Rizwan on batting and he got out on Zero. What is trhe probability that Muhammad Rizwan is;

a) In Category A b) In Category B c) In Category

At a University, the faculty members were surveyed and classified according to Designation and number of research publications during the last Academic year. The data are shown in the Table 6. Research Publications Professor Associate Professor Assistant Professor Lecturer 0 – 2 3 6 16 28 3 – 5 2 4 12 8 More than 5 1 1 4 1 Table 6

If a faculty member is selected at random, find the probability that a) The faculty member have 3 publilcations during last year given that he/she is an Assistant Professor b) The faculty member is Lecturer given that he/she do not have any publication

Larceny and Vandalism A criminology student wishes to see if there is a relationship between the number of larceny crimes and the number of vandalism crimes on college campuses in southwestern Pennsylvania. The data are shown. Is there a relationship between the two types of crimes?

Number of larceny crimes x

24

6

16

64

10

25

35

Number of vandalism crimes y

21

3

6

15

21

61

20

(The information in this exercise will be used for Exercise 17 of Section 10–2.)

a. Draw the scatter plot for the variables.

b. Compute the value of the correlation coefficient.

c. State the hypotheses.

d. Test the significance of the correlation coefficient at a = 0.05, using Table I.

e. Give a brief explanation of the type of relationship.

If the license plates in a Karachi consist of three letters followed by three numbers, what is the probability that a randomly generated plate ends in the numbers “786”? Consider that repetitions are allowed and order matters.

A University wishes to hire 4 faculty members for its newly established department. They have to select from a group of 8 Male and 7 Female applicants, all of whom are equally qualified to fill in the positions. If University selects 4 at random, what is the probability that:
a) All four will be Men
b) All four will be Women
c) Atleast one will be a Women
d) Atleast one will be a Men

These reaction times (in tenths of a second) were recorded for group of subjects after each had been given in a drug pain.

Drug A Drug B Drug C
4 9 8
7 11 6
6 12 7
3 8 6
4 10 5
3 11 7

1. Formulate the H0, and H1:
2. C.V. at alpha .01 level of significance
3. Compute the test value: ANOVA - F ratio
4. Decision
5. Interpretation

In a local referendum to legalize the sale of beer, voters were surveyed about their opinions on the referendum and their views on the moral issue of selling alcohol beverages. From the contingency table, test at 0.05 alpha whether their moral values are related to their opinion on the referendum:



Opinion on referendum



Drinking is :



For Against Undecided

OK

95

83

21

Tolerated

73

71

18

Immoral

12

46

8



Formulate the H0 and H1
C.V. at alpha 0.05 level of significance
Compute the test value: Chi-square X2
Decision
Interpretation