(a) A type of lightbulb is labeled as having an average lifetime of 1000 hours. It's reasonable to model the probability of failure of these bulbs by an exponential density function with mean u 1000(i) Use this model to find the probability that a bulb fails within the first 300 hours. (Round your answer to three decimal places.)(ii) Use this model to find the probability that a bulb burns for more than 700 hours. (Round your answer to three decimal places.)(b) What is the median lifetime of these lightbulbs? (Round your answer to one decimal place.)hr According to the National Health Survey, the heightsadult males in the United States are normally distributed with mean 69.0 inches and standard deviation 2.8 inches.(a) What is the probability that an adult male chosen at random is between 67 and 71 inches tall? (Round your answer to three decimal places.)(b) What percentage of the adult male population is more than 6 feet tall? (Round your answer to one decimal place.)

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Asked Oct 15, 2019
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Answer the 2 parts of the question attached as images.

(a) A type of lightbulb is labeled as having an average lifetime of 1000 hours. It's reasonable to model the probability of failure of these bulbs by an exponential density function with mean u 1000
(i) Use this model to find the probability that a bulb fails within the first 300 hours. (Round your answer to three decimal places.)
(ii) Use this model to find the probability that a bulb burns for more than 700 hours. (Round your answer to three decimal places.)
(b) What is the median lifetime of these lightbulbs? (Round your answer to one decimal place.)
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(a) A type of lightbulb is labeled as having an average lifetime of 1000 hours. It's reasonable to model the probability of failure of these bulbs by an exponential density function with mean u 1000 (i) Use this model to find the probability that a bulb fails within the first 300 hours. (Round your answer to three decimal places.) (ii) Use this model to find the probability that a bulb burns for more than 700 hours. (Round your answer to three decimal places.) (b) What is the median lifetime of these lightbulbs? (Round your answer to one decimal place.) hr

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According to the National Health Survey, the heights
adult males in the United States are normally distributed with mean 69.0 inches and standard deviation 2.8 inches.
(a) What is the probability that an adult male chosen at random is between 67 and 71 inches tall? (Round your answer to three decimal places.)
(b) What percentage of the adult male population is more than 6 feet tall? (Round your answer to one decimal place.)
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Image Transcriptionclose

According to the National Health Survey, the heights adult males in the United States are normally distributed with mean 69.0 inches and standard deviation 2.8 inches. (a) What is the probability that an adult male chosen at random is between 67 and 71 inches tall? (Round your answer to three decimal places.) (b) What percentage of the adult male population is more than 6 feet tall? (Round your answer to one decimal place.)

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Step 2

a).

Let X is the life time of a light bulb follows an exponential distribution with mean 1000 hours.

The probability density function of an exponential distribution with the parameter is given below:

The mean of an expon...

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1 P(x)exp =1000 300 1 P(x 300)=exp " c P(x>700) = [-exp 700 LL ר 300 e 700 300 1000 700 eo 1000 e -e 1-e-03 -0.7 = e =1-0.740 =0.496 =0.260 L

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