Question

In: Statistics and Probability

A manufacturer of compact fluorescent light bulbs advertises that the distribution of the lifespans of these...

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?
(please round to four decimal places) (b) Describe the distribution of the mean lifespan of 15 light bulbs.

  • approximately normal with μ = 9000 and σ=1000√15σ=100015
  • approximately normal with μ = 9000 and σ = 1000
  • left skewed
  • right skewed

(c) What is the probability that the mean lifespan of 15 randomly chosen light bulbs is more than 10,500 hours?
(please round to four decimal places)

Solutions

Expert Solution

Solution: Here concept of normally distributed random variable is used.

Please rate the answer. Thank you.


Related Solutions

Compact fluorescent bulbs are much more efficient at producing light than are ordinary incandescent bulbs. They...
Compact fluorescent bulbs are much more efficient at producing light than are ordinary incandescent bulbs. They initially cost much more, but last far longer and use much less electricity. According to one study of these bulbs, a compact bulb that produces as much light as a 100 W W incandescent bulb uses only 23.0 W W of power. The compact bulb lasts 10000 hours, on the average, and costs $ $ 11.00, whereas the incandescent bulb costs only $ $...
A light-bulb manufacturer advertises that the average life for its light bulbs is 900 hours. A...
A light-bulb manufacturer advertises that the average life for its light bulbs is 900 hours. A random sample of 15 of its light bulbs resulted in the following lives in hours.                          995 590 510 539 739 917 571 555                          916   728   664   693   708   887   849 At the 10% significance level, test the claim that the sample is from a population with a mean life of 900 hours. Use the P-value method of testing hypotheses. Identify the null and alternative hypotheses,...
Compact fluorescent bulbs are much more efficient at producinglight than are ordinary incandescent bulbs. They...
Compact fluorescent bulbs are much more efficient at producing light than are ordinary incandescent bulbs. They initially cost much more, but last far longer and use much less electricity. According to one study of these bulbs, a compact bulb that produces as much light as a 100 W incandescent bulb uses only 23.0 W of power. The compact bulb lasts 1.00×104 hours, on the average, and costs $ 12.0 , whereas the incandescent bulb costs only 75.0 ¢, but lasts...
Q6. A Light bulb manufacturer warrantees that the life of bulbs has normal distribution with       ...
Q6. A Light bulb manufacturer warrantees that the life of bulbs has normal distribution with        average life (μ) of 400 hours and standard deviation (σ) 20 hours. A customer selects one bulb        randomly from the received shipment and installs it under the ceiling of the house. The true        statement (s) that the installed bulb will continue to burn for at least for 482 hours is/are:        a. It is rare but not impossible that bulb will continue...
A manufacturer of light bulbs claims that the average lifetime of one of their bulbs is...
A manufacturer of light bulbs claims that the average lifetime of one of their bulbs is more than 900 hours. A consumer advocacy group wants to test this claim. They obtained a simple random sample of 61 bulbs and timed how long they took to burn out. They obtained a sample mean of 907.5 hours with a standard deviation of 16.5 hours. It’s your job to test the claim at the 5% significance level and determine if the manufacturer is...
A manufacturer of light bulbs claims that its light bulbs have a mean life of 1520...
A manufacturer of light bulbs claims that its light bulbs have a mean life of 1520 hours. If a random sample of 40 bulbs is tested and has an average life of 1500 hours and the standard deviation is 80 hours, is there sufficient evidence to claim that the mean life is different than the manufacturer's claim? Use alpha = 0.01. Calculate the test statistic. Calculate a confidence interval for the true mean light bulb life. Use the level of...
Feit Electric manufactures 60-watt equivalent Compact Fluorescent Bulbs that it guarantees will last at least 10,000...
Feit Electric manufactures 60-watt equivalent Compact Fluorescent Bulbs that it guarantees will last at least 10,000 hours. The Consumer Testing Company tested the claim of the manufacturer by purchasing a random sample of 60-watt equivalent CFBs manufactured by Feit Electric. The Consumer Testing Company tested 36 CFBs. The results of the test are found in Chapter_10_Project_HT_CFB.xlsx. The Consumer Testing Company has no other data on CFBs from the manufacturer, so must rely for its test on the sample of 36...
GreenBeam Ltd. claims that its compact fluorescent bulbs average no more than 3.41 mg of mercury....
GreenBeam Ltd. claims that its compact fluorescent bulbs average no more than 3.41 mg of mercury. A sample of 45 bulbs shows a mean of 3.46 mg of mercury. (a) State the hypotheses for a right-tailed test, using GreenBeam’s claim as the null hypothesis about the mean. a. H0: μ ≥ 3.41 mg vs. H1: μ < 3.41 mg b. H0: μ ≤ 3.41 mg vs. H1: μ > 3.41 mg c. H0: μ = 3.41 mg vs. H1: μ...
A manufacturer claims that the mean lifetime of its fluorescent bulbs is 1300 hours. A homeowner...
A manufacturer claims that the mean lifetime of its fluorescent bulbs is 1300 hours. A homeowner selects 25 bulbs and finds the mean lifetime to be 1270 hours with a standard deviation of 80 hours. Test the manufacturer's claim. Use α = 0.05.
A manufacturer claims that the mean lifetime of its fluorescent bulbs is 1000 hours. The lifetimes...
A manufacturer claims that the mean lifetime of its fluorescent bulbs is 1000 hours. The lifetimes are normally distributed with a standard deviation of σ = 80 hours. A homeowner decides to test the manufacturer's claim; in a random sample of 40 bulbs, the mean lifetime is 980 hours. At a significance level of α = 0.05, does this data provide evidence to reject the manufacturer's claim? Show all 7 steps for p-value method.
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT