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# Density Functions: Time takes students to finish aptitude test

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1. The time it takes for a student to finish an aptitude test has the density function
f(x) = c(x-1) (2-x), 1<x<2
= 0, otherwise.
Here the unit of time is an hour.
a) Evaluate the Normalizing constant c.
b) Plot the density function
c) Calculate the probability that a student will finish the test in less than 75 minutes
d) Calculate the probability that a student will finish the test between 1.5 and 2 hours.

2. For the density f(x) = 375/(x^4), for x>5 and zero otherwise.
a) Find the median
b) Find the 90th percentile
c) Find the 10th percentile

3. Let f(x) be the uniform density on [0,1] and let g(x) be the density on [0,1] given by g(x)=ce^x, where c is the normalizing constant. Let F, and G be the corresponding CDFs. Find the density function corresponding to the new CDF H(x) = F(x)G(x).

https://brainmass.com/statistics/probability-density-function/density-functions-time-takes-students-finish-aptitude-test-388731

#### Solution Preview

1. The time it takes for a student to finish an aptitude test has the density function
f(x) = c(x-1) (2-x), 1<x<2
= 0, otherwise.
Here the unit of time is an hour.
a) Evaluate the Normalizing constant c.
b) Plot the density function
c) Calculate the probability that a student will finish the test in less than 75 minutes
d) Calculate the probability that a student will finish the test between 1.5 and 2 hours.
Solution
a) Since is a probability density function we have

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Therefore, ...

#### Solution Summary

The expert determines the time it takes for students to finish aptitude tests.

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