1-In a paint production line, the density of these corresponds to a continuous random variable with values ??that are in the range of 1.2 to 1.8 g/cm3

It has been determined that the probability density function of this variable should have the form:

f(x)=kx2

Based on this information, determine:

a. The value of k (in fraction) (8 points)

b. The probability that the density is greater than 1.6 g/cm3 (8 points)

c. The expected value of the density of the paints. (8 points)

develop the questions

2- A study of the time (in hours) college freshmen spend studying each week revealed the mean to be 4.5 hours and the variance to be 9 hours. If a group of 80 freshmen is chosen, determine the percentage of students who:

a) They study at least 5 hours (6 points)

b) They study at most 6 and a half hours. (8 points)

c) They study between 4 and 7 hours. (10 points)

(use two decimals with the last approximate, to work with the table)

Note: Express your final answer as a percentage to two decimal places, example: 10.56% develop the questions.

3. Let the random variable be X= Number of programs contracted by a client to his cable company. Randomly selected and considering the following probability function::