Statistics and Probability Answers

1. An analysis of monthly wages paid to the workers in two company X and Y gives the following results:  

                                                                      Firm X                Firm Y 

Number of worker:                            45                    50 

Average monthly wages in $:            100                  120  

Variance of distribution of wage:       49                     36             

1. Which company, X or Y, has a large wage bill? 
2. In which company, X or Y is there grater variability in wage? 
3. Calculate combined mean wage of company X and Y

Each item coming off a given production line is inpected by either inspector 1 or inspector 2. Inspector 1 inspects about 60% of the production items, while inspector 2 the rest. Inspector 1, who has been at her present job for some time, will not find 1% of the defective items she inspects. Inspector 2, who newer on the job, misses about 5% of the defective items he inspects. If an item that has passed an ispector is found to be defective, what is the probability that it was inspected by inspector 1?

An experiment is run in the following manner. The colors red, yellow, and blue are each flashed on a screen for a short period of time. A subject views the colors and is asked to choose the one he feels was flashed for the longest amount of time. The experiment is repeated three times with the same subject. If all the colors were flashed for the same length of time, give the probability distribution for y, the number of times the subject choose the color red. Assume that his three choice are independent.

A sample of size 10 drawn from a normal population has a mean 31 and a variance 2.25. Is it reasonable to assume that the mean of the population is 30? 

(Use 1% level of significance, given that P(|t| )=0.1, for 9 d.f)

1.   The mean annual wage of male workers in a particular company was Ksh. 67952 and that of female workers was Ksh. 61295 each year. The standard deviation for the two samples is Ksh. 3202 and Kshs.3758, respectively. Assuming the measurements are from random samples of 24 males and 27 we want to investigate whether the mean salary of males is higher than that of females at α=0.05. Find:

a.      The test statistic

b.     Remember that the Null hypothesis will be rejected if . Give the value of

The random variable J has a geometric distribution and it is given that, 𝑃(𝐽=5)/𝑃(𝐽=7) = 25/16 .

Find 𝑃(𝐽 = 4)

A mechanic performs MOT tests on cars to see if they are roadworthy, and only 75% of cars pass this test  If 10 cars are tested one day, find the probability that 8 or more cars pass the test.

Let 𝑋 be the number of times an ordinary fair die is rolled, up to and including the roll on which

the first prime number is obtained.

Find the mode of 𝑋

Find 𝐸(𝑋)

Evaluate 𝑃(𝑋 > 𝐸(𝑋))

You are working for a bank. The bank manager wants to know the mean waiting time for all 

customers who visit this bank. She has asked you to estimate this mean by taking a sample. 

Briefly explain how you will conduct this study. Assume the data set on the waiting times for 

10 customers who visit a bank. Then estimate the population mean. Choose your own 

confidence level. 

 Each item coming off a given production line is inpected by either inspector 1 or inspector 2. Inspector 1 inspects about 60% of the production items, while inspector 2 the rest. Inspector 1, who has been at her present job for some time, will not find 1% of the defective items she inspects. Inspector 2, who newer on the job, misses about 5% of the defective items he inspects. If an item that has passed an ispector is found to be defective, what is the probability that it was inspected by inspector 1?