# Random Sample

Find the probability and the z-value for the questions attached.

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#### Solution Summary

The solution addresses the following:

? A software distributor is considering whether to purchase a batch of 20,000 3.5" floppy disks at a flea market auction for 4 cents each. The disks were originally guaranteed by the manufacture to be only 5% defective, but no returns are allowed at this price. Before rushing to make a payment, the distributor decided to select a random sample of 20 disks to investigate the quality claim anyway. After all, too many defective disks (over 10%) rule out the purchase, irrespective of the bargain price.

a. What is the probability that no defective disks are found in the sample?

b. What is the probability that 3 or more defective disks are found in the sample?

c. What is the probability that less than 2 defective disks are found in the sample?

d. What is the probability that all the disks in the sample are defective?

e. If 3 defective disks are found in the sample, what can you conclude about the original guarantee?

? Suppose that 40% of a population have blue eyes. The number of people with blue eyes in a sample of 600 has a binomial distribution. The mean of the distribution is 240, and the standard deviation is 12. True or False

?

The average speed of all vehicles on a highway is 65 and the standard deviation is 4. If the speeds are normally distributed, a car traveling 73 has a z-score of 2. True or False

? If P(X>x)=0.34 and P(X=x)=0.10, thenP(<_x)=0.56 true or flase

? A sample of 25 electric motors is taken from a large lot. The average current drawn by each motor at rated speed and RPM is 7.65 amps. The standard deviation of the sample is 0.15 amps. If the motor are rated on the stamped nameplate as drawing 7.5 amps,what is the z-score for this sample?

Random Sample

A recent article in Buisness Week listed the best small companies. We are interested in the current results of the companies sales and earnings. A random sample of 12 companies was selected and the sales and earnings, in millions of dollars, are reported below.

Company Sales Earnings

($ millions) ($ earnings)

Papa John's International 89.2 4.9

Applied Innovation 18.6 4.4

Integracare 18.2 1.3

Wall Data 71.7 8.0

Davidson Associates 58.6 6.6

Chico's Fas 46.8 4.1

Company Sales Earnings

($ millions) ($ millions)

Checkmate Electronics 17.5 2.6

Royal Grip 11.9 1.7

M-Wave 19.6 3.5

Serving-N-Slide 51.2 8.2

Daig 28.6 6.0

Cobra Golf 69.2 12.8

Let sales be the independent variable and earnings be the dependent variable.

A. Draw a scatter diagragm.

B. Compute the co-efficient of correlation.

C. Compute the co-efficient of determination.

D. Interpret your findings in part B and C.

E. Determine the regression equation.

F. for a small company with 50.0 million in sales, estimate the earnings.

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