Statistics and Probability Answers

a. Using the provided information below,

x=33.2, x2=131.67, y=30.78 , y2=116.52 , xy=119.8 , and n=10

i. Find the sample correlation coefficient r

ii. Find the co-efficient of determination

1. A certain store has four ways of handling returns: cash refund, credit to account, exchange, or refusal. The manager claims that the four ways are equally probable.to test this hypothesis, 108 customers were sampled with the following results

Type Cash Credit exchange Refusal

Count 34 27 32 15

Does the data support the manager’s claim at 5 %.

A survey of middle-aged men reveals that 28% of them are balding at the crown of their

heads. Moreover it is known that such men have an 18% probability of suffering a heart

attack in the next ten years. Men who are not balding in this way have an 11% probability of

a heart attack. Find the probability that a middle-aged man will suller a heart attack sometime in the next 10 years

Consider all samples of size 5 from this population:6 8 10 12 13

1. Compute the mean and variance of the population

2.list all samples of size 4 and compute the mean for each sample

3.construct the sampling distribution of the sample means

4.Calculate the mean of the sampling distribution of the sample means and compare this to the mean of the population

sketch the normal curve and find the area in each of the following cases 

1. between z=-2.76 and z= -1.2

2. To the right of z=1.31

3. To the left of z=0.35

4.to the right of z= -0.95

When do we add the corresponding area of the z-score to 0.50?

A green urn contains three red balls and five black balls. A blue urn contains three red balls and seven black balls. A yellow urn contains two red balls and four black balls.

1. If an urn is selected at random and a ball is drawn, then the probability that it will be red is .
2. If a red ball is selected, then the probability that the green urn is selected is .
3. If the person drawing a ball from an urn favors choosing the yellow urn twice more than the green urn and thrice more than the blue urn, then the probability of drawing a red ball is .

Between z=-1.46 and z=2.15

Task 4 make your own experiment and trial .choose your own random variable X and compute for its mean , variance and standard deviation

A population consists of the five numbers: 2,3,6,8 and 11. Consider samples of size 2 that can be drawn from this population. 1. List all the samples and the correspondinv mean. 2. Construct tha sampling distribution of the sample mean. 3. Draw a histogram of the sampling distribution of the mean.