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# Probability Problems

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Need step by step answer to Q no. 2,3 and 7.

Please note for Q#3 that only the exponent of e is divided by 2b^2, not the entire numerator as it seems in question.

See attached file for full problem description.

https://brainmass.com/statistics/probability-density-function/probability-problems-procedure-computations-116027

#### Solution Preview

Since f(x) is a density function ,we have
Thus
Thus k/8=1
k=8

Mean is given by E(X)= =
= 0.443113
Where Erf(x) is the integral of the Gaussian ...

#### Solution Summary

Calculation of covariance, marginal probability, expectation, probability density function, log normal distribution. The answers are given with interpretation of results.

\$2.19
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## 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?

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