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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).

##### Solution Summary

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

##### 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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##### Measures of Central Tendency

This quiz evaluates the students understanding of the measures of central tendency seen in statistics. This quiz is specifically designed to incorporate the measures of central tendency as they relate to psychological research.