Find Probabilities, Mean and Standard Deviation, and Distribution
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1. The number of hours needed by students in an economics course to complete a term paper are attached.
A student is selected at random. Find the following probabilities.
a. the student took more than 9 hours
b. the student took less than 6 hours
c. the student took between 7 and 9 hours, inclusive.
2. A box holds 5 blue chips, 14 orange chips, and 6 yellow chips. If a chip is randomly selected, what is the probability that it is yellow?
3. A company makes batteries in batches of 20, with a 3% rate of defects. Find the mean and standard deviation for the random variable x, the number of defects per batch.
4. Find the mean and standard deviation for the random variable x, given the attached distribution
5. The variable x is normally distributed. The mean is 15.2, and the standard deviation is 0.9. if an item is randomly selected, find the probability that it is greater than 16.1.
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Solution Summary
This solution is provided in an attached .doc file. It goes through each question and briefly calculates and explains how to calculate probability, mean and standard deviation.
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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