Graded Problem Set #6 - Done.docx - MTH 243 – PCC(Trude Name_Jin Situ GRADED PROBLEM SET#6 Answer each of the following questions completely There are

Graded Problem Set #6 - Done.docx - MTH 243 – PCC(Trude...

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MTH 243 – PCC (Trude) Name:___________Jin Situ______ _______ GRADED PROBLEM SET #6 Answer each of the following questions completely. There are a total of 20 points possible in the assignment. 1. A manufacturer of compact fluorescent light bulbs advertises that the distribution of the lifespans of these light bulbs is nearly normal with a mean of 9,000 hours and a standard deviation of 1,000 hours. a. What is the probability that a randomly chosen light bulb lasts more than 10,500 hours? P(X >10500) =P(Z >(10500−9000)/1000)=P(Z >1.5)= 0.0668 The probability that a randomly chosen light bulb lasts more than 10,500 hours is 6.68%. b. What is the probability that the mean lifespan of 15 randomly chosen light bulbs is more than 10,500 hours? _ P( X >10500) =P(Z >(10500−9000)/(1000/√15))=P(Z >5.81)= 0 The probability that the mean lifespan of 15 randomly chosen light bulbs is more than 10,500
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Unformatted text preview: hours is 0. c. Could you estimate the probabilities from parts a and b if the lifespans of light bulbs had a skewed distribution? Explain. If the lifespans of light bulbs had a skewed distribution then we should not estimate the probabilities in parts a or b using the normal distribution. In part a, we would need to use the skewed distribution to do the probability calculations. In part b, because n = 15<30, it already out of normally distributed of 30. 2. The Pew Research Center estimates that as of January 2014, 89% of 18-29 year olds in the United States use social networking sites. Calculate the probability that at least 91% of 500 randomly sampled 18-29 year olds use social networking sites. MTH 243 – PCC (Trude) Name:___________Jin Situ______ _______...
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