Question

An ice cream seller takes 20 gallons of ice cream in her truck each day. Let X stand for the number of gallons that she sells. The probability is 0.1 that X = 20. If she does not sell all 20 gallons, the distribution of X follows a continuous distribution with a p.d.f. of the form
f(x) = {ex 0< x < 20
0, otherwise

Find the constant c.

Answer 1

Considering the given probability distribution, the constant c is given by: c = 0.0045.

How to find the constant c?

We have to consider the distribution given by:

• f(x) = cx, 0 < x < 20.

We have that P(X < 20) = 0.9, and this is represented by the following definite integral:

$P(X < 20) = \int_{0}^{20} cx dx$

Hence, applying the rule for the integral of the power of x, we have that:

$P(X < 20) = 0.5cx²|_{x = 0}^{x = 20}$

Then, applying the Fundamental Theorem of Calculus:

200c = 0.9.

c = 0.9/200

c = 0.0045.

Hence the constant c is given by: c = 0.0045.

More can be learned about probability distributions at brainly.com/question/22583815

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