# Random Sample

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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?

###### Education

- BSc , Wuhan Univ. China
- MA, Shandong Univ.

###### Recent Feedback

- "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
- "excellent work"
- "Thank you so much for all of your help!!! I will be posting another assignment. Please let me know (once posted), if the credits I'm offering is enough or you ! Thanks again!"
- "Thank you"
- "Thank you very much for your valuable time and assistance!"

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