Reference no: EM13654289

Part -1:

1. The following poll shows employees engagement with their work. The study also shows that having more engaged workers leads to increased innovation, productivity and profitability, as well as reduced employee turnover.

                                                            Country

Engagement	USA	Germany	Total
Engaged	550	246	796
Not engaged	1 345	1 649	2 994
Total	1 895	1 895	3 790

If an employee is selected at random, what is the probability that he or she

a) is engaged with his or her workplace
b) is a US worker
c) is engaged with his or her workplace or is a US worker
d) explain the difference in the results in (b) and (c)

2. From the last year's data was found that the pizza restaurant filled the orders approximately 91% correctly. What is the probability that

a) All five orders will be filled correctly
b) None of the five will be filled correctly
c) At least four of the five will be filled correctly

3. For a survey, final exam grades of 100 students are gathered. The mean grade was 28 on a 40 based scale with a standard deviation of 4 Assume that the grades of students are approximately normally distributed. For a randomly selected student what is the probability that he or she scores

a) Below 20?
b) Above 35?
c) Between 25 -35?

4. 10 liter of petrol is put in each of the 30 test autos and the resulting figures are tabulated as follows: mean X = 120 km, s = 15 km. Determine a 99% confidence interval estimate of the mean mileage.

Part -2:

1. The agriculture investment company wants to estimate the mean retail value of lemons. A random sample of 200 stores indicates a mean value of 0.3 AZN with a standard deviation of 0.05 AZN. Assuming a normal distribution, construct a 99% confidence interval estimate for the mean value of lemons on sale

2. The waiting time data (in minutes) in a bank, collected from a sample of 6 customers during the noon-fpm interval is listed below.
5.05      4.80     8.01    8.35    5.70    4.08
Compute the following:

a) The mean, median, mode

b) Range, IQR, variance, standard deviation and coefficient of variation

c) Z scores

3. A sample of 500 purchasing managers was selected to determine information concerning buying behavior. Among the questions asked was "Do you enjoy your role in the organization?" Of 240 males, 136 answered yes. Of 260 females, 224 answered yes. Construct a contingency table to evaluate the probabilities. What is the probability that a respondent chosen at random

a) Enjoys his or her role in the organization?
b) Is a female and enjoys her role in the organization?
c) Is a female or enjoys her role in the organization?
d) Is a male or female?

4. The probability of birth for a girl is 51%. If a family has four children what is the probability that

a) All four are girls?
b) None of them is a girl?
c) At least two of four are boys?