Related questions with answers

Suppose that the counts recorded by a Geiger counter follow a Poisson process with an average of two counts per minute. a. What is the probability that there are no counts in a 30-second interval? b. What is the probability that the first count occurs in less than 10 seconds? c. What is the probability that the first count occurs between one and two minutes after start-up?

Samples of 20 parts are selected from two machines, and a critical dimension is measured on each part. The data are shown next. Plot the data on normal probability paper. Does this dimension seem to have a normal distribution? What tentative conclusions can you draw about the two machines? Machine 1

\begin{matrix} \text{99.4} & \text{101.5} & \text{102.3} & \text{96.7}\\ \text{99.1} & \text{103.8} & \text{100.4} & \text{100.9}\\ \text{99.0} & \text{99.6} & \text{102.5} & \text{96.5}\\ \text{98.9} & \text{99.4} & \text{99.7} & \text{103.1}\\ \text{99.6} & \text{104.6} & \text{101.6} & \text{96.8}\\ \end{matrix}

Machine 2

\begin{matrix} \text{90.9} & \text{100.7} & \text{95.0} & \text{98.8}\\ \text{99.6} & \text{105.5} & \text{92.3} & \text{115.5}\\ \text{105.9} & \text{104.0} & \text{109.5} & \text{87.1}\\ \text{91.2} & \text{96.5} & \text{96.2} & \text{109.8}\\ \text{92.8} & \text{106.7} & \text{97.6} & \text{106.5}\\ \end{matrix}

Hits to a high-volume Web site are assumed to follow a Poisson distribution with a mean of 10,000 per day. Approximate each of the following: a. Probability of more than 20,000 hits in a day b. Probability of less than 9900 hits in a day c. Value such that the probability that the number of hits in a day exceeds the value is 0.01 d. Expected number of days in a year (365 days) that exceed 10,200 hits. e. Probability that over a year (365 days), each of the more than 15 days has more than 10,200 hits.