Descriptive Statistics and Faulty Computers
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A computer laboratory in a school has 33 computers. Each of the 33 computers has a 90% reliability. Allowing for 10% of the computers to be down, an instructor specifies an enrollment ceiling of 30 for his class. Assume that a class of 30 students is taken into the lab.
a. What is the probability that each of the 30 students will get a computer in working condition?
b. The instructor is shocked to see the low value of the answer to (a), and decides to improve it to 95% by doing one of the following:
i. Decreasing the enrollment ceiling.
ii. Increasing the number of computers in the lab.
iii. Increasing the reliability of all the computers.
To help the instructor, find out what the increase or decrease should be for each of the three alternatives.
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Solution Summary
This solution contains step-by-step calculations and explanations to determine probabilities, and how each of the three situations affects how many students get a working computer. All formulas are shown.
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A computer laboratory in a school has 33 computers. Each of the 33 computers has a 90% reliability. Allowing for 10% of the computers to be down, an instructor specifies an enrollment ceiling of 30 for his class. Assume that a class of 30 students is taken into the lab.
a. What is the probability that each of the 30 students will get a computer in working condition?
Denote by X the number of computers in working condition. Then X follows binomial distribution with n=33 and p=0.9. We need to compute .
There are two ways to get this ...
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- 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!"
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