Statistics and Probability Answers

Given a population of the scores of BSHS honor students in Mathematics as 1, 3, 4, 6, and 8. Suppose a sample size of 3 have to be drawn from it for the first, second and third rank;

For normally distributed data, what proportion of observations have a z-score less than 2.74.

What will you add to the following data : 21.5 , 34.6 , 44.8 , 11.3 , 17.9 to get a mean exactly equal to 30.35?

Q_3: Counting Techniques (Multiplication Rule) = 2.5 (1) Researchers at a large training event are offered 5 sightseeing tours on each of 5 days. In how many ways can a person arrange to go on a sightseeing tour planned by this training event? (2a) For the picture shown below, find out in how many ways are possible for IMEI and Serial numbers for a cell phone? If lower case alphabets are also allowed, then how will that change the total ways for the Serial numbers? (2b) For the picture shown below, find out in how many ways are possible for Serial numbers on a US One Dollar Bill? If lower case alphabets are also allowed, then how will that change the total ways for the Serial numbers? (4) In a petrol consumption research, each of 4 sports vehicles is tested using 5 different brands of petrol at 5 test sites located in different locations of Karachi. If 3 drivers are used in the research, and test runs are made once under each distinct set of conditions, how many test runs are needed?

Q_2: = 2.5 An experiment consists of rolling a die and then tossing a coin once if the number on the die is even. If the number on the die is odd, the coin is tossed twice. Using the notation 4H, for example, to denote the outcome that the die comes up 4 and then the coin comes up heads, and 3HT to denote the outcome that the die comes up 3 followed by a head and then a tail on the coin, construct a tree diagram to show the elements of the sample space S. (1) List the elements corresponding to the Event-A that a number less than 3 occurs on the die (2) List the elements corresponding to the Event-B that two tails occur (3) List the elements corresponding to the Event (4) List the elements corresponding to the Event ∩B (5) List the elements corresponding to the Event A ⋃ B

The standard deviation of a population is 2.50 cms. What is the probability that in a random sample of size 100 the sample mean will differ from the population mean by 0.75 or more?

Select one:  a. 0.9974  b. 0.0013  c. 0.9987  d. 0.0026 

To test the hypothesis that the coin is fair, the adopted rule is: "accept the hypothesis if the number of heads in 10 tosses is more than 4". Then find the probability of committing type I error.

Select one:  a. B(4;10;0.5)  b. B(3;10;0.5)  c. B(5;10;0.5) d. B(2;10;0.5) 

Let p be the probability that a coin will fall head in a single toss in order to test Ho : p = 1/2 against H_1:p=3/4. The coin is tossed 5 time and Ho is rejected if more than 3 heads obtained. Find the level of significance

Select one:  a. 3/16  b. 3/64  c. 3/32  d. 1/2 

The mean weight of luggage checked by a randomly selected economic class passenger flying between two cities on a certain airline is 40Ib, and the standard deviation is 10 lb. The mean and standard deviation for a business class passenger are 30lb and 6 lb respectively. If there are 50 economic class and 12 business class passengers on the flight, what is the variance of total luggage weight?

Select one:  a. 2360  b. 5000  c. 432  d. 5432