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Calculating Probabilities for Product Performance

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#1
The average life of a light bulb is 500 hours. Find

a) The probability that a bulb will last more than 1,000 hours
b) The probability that a bulb will last less than 100 hours
c) The median life
d) The probability that a bulb will last exactly 500 hours
e) The 95 Percentile

(Note e^ (-3.0) is almost 0.05, so the 95 percentile life would be -3.0/0.002 = 1,500 hours)

#2

An elevator has a design capacity of 2,560 pounds and a posted limit of 16 passengers. The weight of adults is approximately normal with a mean of 150 pounds and standard deviation of 20 pounds.

Find the probability that the elevator will be overloaded if 16 people are in the elevator. How many passengers would you recommend if you wanted to be sure that the overloading probability is less than 0.001?

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Solution Summary

This solution contains over 300 words and calculations to aid you in understanding the probabilities for product performance.

Solution provided by:
Changping Wang, MA
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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