QANT 201 Statistical Sampling Theory Question 11): The mean Iifespan of a standa
ID: 3361553 • Letter: Q
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QANT 201 Statistical Sampling Theory Question 11): The mean Iifespan of a standard 75-watt incandescent light buitb is 875 hours with a standard deviation of 80 hours. The mean lifespan of a st Fluorescent light bulb (CFL) is 10,000 hours with a standard deviation of 1,500 hours. These two bulbs put out about the same amount of light. Assume the lifespans of both types of bulbs are normally distributed to answer the following questions (a) I select one incandescent light bulb and put it in my Apartment. It seems to last forever, and I estimate that it has lasted more than 2000 hours. What is the probability of selecting a random incandescent light bulb and having it last 2000 hours or more. Did something unusual happen here? (b)I select one CFL bulb and putit in the bathroom. t doesn't seem to last very long, and I estimate that it has lasted less than 5,000 hours. What is the probability of selecting a random CFL and having it last less than 5,000 hours. Did something unusual happen here? (c) Compare the lifespan of the middle 99% of all incandescent and CFL light bulbs. (Hint: a2 -2.575)Explanation / Answer
A) P(X > 2000) = P ((X - mean)/(SD) > (2000 - mean)/(SD)
= P(Z > (2000 - 875)/80
= P(Z > 14.06)
= 1 - P(Z < 14.06)
= 1 - 1 = 0
As the probability is less than 0.05 so it is unusual.
B) P(X < 5000) = P ((X - mean)/SD < (5000 - mean)/sd)
= P(Z < (5000 - 10000)/1500)
= P(Z < -3.33)
= 0.0004
C) At 99% cinfidence interval the critical value is 2.575
For incandescent light the Confidence interval is
Mean +/- z* * SD/sqrt (n )
= 875 +/- 2.575 * 80/sqrt(1)
= 875 +/- 206
= 669, 1081
For CFL light bulb the Confidence interval is
Mean +/- z* * SD/sqrt (n )
= 10000 +/- 2.575 * 1500/sqrt(1)
= 10000 +/- 3862.5
= 6137.5, 13862.5
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