manufacturer of 8-watt LED downlights has past data that shows the lifespan of the downlight is normally distributed with mean 50,000 hours and standard deviation 5,000 hours. Let ? be the lifespan of a random selected LED 8-watt downlight from this manufacturer. a. Identify the distribution of X and state the value/s of its parameter/s. b. What is the probability that a randomly selected 8-watt LED downlight lasts more than 60,000 hours? c. What proportion of randomly selected 8-watt LED downlights have a lifespan between 40,000 and 55,000 hours?
A manufacturer of 8-watt LED downlights has past data that shows the lifespan of the
downlight is
Let ? be the lifespan of a random selected LED 8-watt downlight from this manufacturer.
a. Identify the distribution of X and state the value/s of its parameter/s.
b. What is the probability that a randomly selected 8-watt LED downlight lasts more than
60,000 hours?
c. What proportion of randomly selected 8-watt LED downlights have a lifespan between
40,000 and 55,000 hours?
d. Find the minimum lifespan of the top five percent of the 8-watt LED downlights produced by this manufacturer.
e. Explain in simple language what information your answer in part d. provides to the
consumer.
f. Verify your answers to parts b., c., and d. using the appropriate Excel statistical
and demonstrate you have done this by including the Excel formula used.
g. A random sample of twenty-five 8-watt LED downlights produced by this manufacturer is
selected. State the type of distribution and the value/s of the parameter/s for the mean of
this sample.
h. Calculate the probability that the average lifespan of this sample is less than 47,500 hours.
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