The number of hits on a certain website follows a Poisson distribution with unkn

Question

The number of hits on a certain website follows a Poisson distribution with unknown mean per minute. In order to estimate the mean they counted the number of hits in an hour. They counted 180 hits in 60 minutes. a. Estimate the average number of hits in a minute. b. Find the uncertainty in that estimate. c. Find the probability that they received zero hits in a given minute. d. Find the uncertainty in the probability found in part (c). The lifetime of a light bulb in a certain application is normally distributed with mean mu = 1400 hours and standard deviation sigma = 200 hours. a. What is the probability that a light bulb will last more than 1800 hours? b. Find the 95^th percentile of the lifetimes.

Explanation / Answer

6.

Params of normal distribution:

Mean = 1400

Stdev = 200

a. P(X>1800) = P(Z>2) = .0225

b.

95th percenitle is Z=1.645 from Z tables.
So, X = Z*Sigma+mean = 1.645*200+1400 = 1729

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