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# Probability

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The human resource director of Sunshine Corporation uses a paper-pencil test that measures work habits to help decide whom to hire. From her past research with the company, she has found the correlation-for those who are hired-between the work-habits inventory and a job performance scale after one year to be +.80. She decides to use the work-habits inventory as a selection device for hiring. The mean of the work-habits inventory = 25, standard deviation (SD) = 6; for job performance, the mean = 5 and the SD = 1.8.
1) Trina, a prospective employee, receives a score of 27 on the work-habits inventory. What is her predicted job performance scale score?

2) Rolando, another prospective employee, 'receives a score of 14 on the work-habits inventory.
What is his predicted job performance scale score?

3) If we assume that the work-habits inventory scores are normally distributed, what is the probability that someone would score 10 or lower?

4) You have a friend who is conducting a research study and wants to make sure that the religious affiliation of her sample is representative of the population she is interested in studying. What type of sampling technique would you suggest she use, and why?

5) You are extremely bored one night and decide to go to the Isle of Capri Casino in Boonville, Missouri, for fun (you're really bored) You decide to play some roulette but are only going to bet on "red" or "black" (you're betting that the marble will land on either a red or black number) After betting on black six times in a row and losing six times in a row, you're convinced that the odds are in your favor that the next spin will result in black winning. Please describe the error in your thinking.
6) You and three friends are all taking the same statistics course. Assuming that each of you has a probability of .75 of getting an A in the course, what is the probability that all four of you . will get As (assuming that the probability of each one of you getting an A is independent of each other)'!

7) You and another friend are taking a math course together, and the probability that you will get an A is.80, but your friend's probability is only .45. What is the probability that either one of you will get an A?

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The answers are also in the attached file:

The human resource director of Sunshine Corporation uses a paper-pencil test that measures work habits to help decide whom to hire. From her past research with the company, she has found the correlation-for those who are hired-between the work-habits inventory and a job performance scale after one year to be +.80. She decides to use the work-habits inventory as a selection device for hiring. The mean of the work-habits inventory = 25, standard deviation (SD) = 6; for job performance, the mean = 5 and the SD = 1.8.

We have to calculate the regression equation: Y = a + b X (a= intercept; b= slope)
where Y = Job performance, X = Work-habits inventory

Y = Job performance score
mean= 5
standard deviation= 1.8

X = Work-habits inventory
mean= 25
standard deviation= 6

Correlation between X and Y = 0.80

slope of the regression equation b= correlation x standard deviation of Y / standard deviation of X= 0.24 =0.8x1.8/6

Y mean = a + b X mean
or
5 = a+ 0.24 x 25
or a= -1 =5-0.24x25

Therefore, the regression equation is Y= -1 + 0.24 X

1) Trina, a prospective employee, receives a score of 27 on the work-habits ...