9) A concrete plant takes 20 independent samples of concrete each month. The sam

Question

9) A concrete plant takes 20 independent samples of concrete each month. The samples are cured and strength tested to evaluate quality control at the plant. Let N2o be the number of samples which fall below a strength of 20 MPa. In general the fraction of such low strength sampl ???? ENGM2032, Applied Probability and Statistics Assignment #3 Summer 2017: p83 around 10%, and this is considered acceptable. However, if the samples taken in a particular month yield a value of Nzo which exceeds its mean by more than two standard deviations, the plant operations are critically reviewed. a) What is the probability of having to critically review the plant operations even though the actual fraction of low strength samples for that month is still 10%? b) If the actual fraction of low strength samples remains at 10%, what is the probability that the next critical review will take place in exactly 5 months?

Explanation / Answer

a) The distribution is not known so we can used Chebyshev's inequality to find the probability.

So probability of having to critically review the plants operations even though the actual fraction of low strength samples for that month is still 10% is 1/(K2 )

Here K = number of units of standard deviation far from mean = 2

So that required probability = 1/4 = 0.25

b) If X is the random variable which takes the values of number of sample required to show critical review.

When process is in control then X follows geometric distribution with probability of success = p = 0.25

So that P(X = 5) = p *(1 - p)^5 = 0.25 *0.754 = 0.079102

Then P(X =5)

Related Questions

Navigate

• Browse (All)
• Browse 9
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.