# Probability problem

The number of failures of a unit from contamination particles on the unit is a Poisson random variable with a mean of 0.02 failures per hour.

a.) What is the probability that the instrument does not fail in an 8-hour shift?

b.) What is the probability of at least one failure in a 24-hour day?

Samples are defective in 1% of cases. Suppose 15 samples are studied, and they can be considered to be independent for being defective. Determine the following probabilities. Use the binomial table to help.

a.) No samples are defective.

b.) At most one sample is defective.

c.) More than half the samples are defective.

https://brainmass.com/statistics/probability-density-function/probability-unit-contamination-particles-144352

#### Solution Preview

Please see the attached file.

The number of failures of a unit from contamination particles on the unit is a Poisson random variable with a mean of 0.02 failures per hour.

a.) What is the probability that the instrument does not fail in an 8-hour shift?

Let T be the time of first failure. The probability density function of T is given by . This density is said to have the exponential distribution with rate ...

#### Solution Summary

This solution gives the step by step method for computing probability.

Three questions on probability

1) Researchers at a pharmaceutical company have found that the effective time duration of a safe dosage of a pain relief drug is normally distributed with mean 2 hours and standard deviation 0.3 hour. For a patient selected at random:

a) What is the probability that the drug will be effective for 2 hours or less?

b) 1 hour or less?

c) 3 hours or more?

2) Life span for red foxes follow an approximately normal distribution with mean 7 years and standard deviation 3.5 years.

a) Find the probability that a red fox chosen at random will live at least 10 years.

b) Find the probability that a random sample of 4 red foxes will have a sample mean life span of over 10 years.

3) Margot has found that the mean time to run a job at the college copy center is 12.6 minutes with standard deviation 10 minutes. She selects a random sample of 64 jobs.

a) What is the probability that the sample mean copying time is between 14 and 15 minutes?

b) What is the probability that the sample mean copying time for this sample is between 10 and 12 minutes?