Question

The manager of a local soft drink company believes that when a new beverage dispensing machine is set to dispense 7 ounces, it in fact dispenses an amount X at random anywhere between 6.5 and 7.5 ounces. Suppose that X has a uniform distribution.

Please answer with detailed working

a) Find P (X > 7.1)

b) Find P (6.85 < X < 7.25)

c) If you pick five bottles at random, what is the probability that exactly three bottles will contain more than 7.1 ounces?

Answer 1

This is a uniform distribution with

Since we know that
Probability density function of a uniform distribution is

This implies that
Cummulative density function of a uniform distribution is


a) Pr(X>x) = 1- F(x)
Where x = 7.1


b) Pr(x1<X<x2) = F(x2) - F(x1)
Where x1 = 6.85 & x2 = 7.25

c) This is a binomial distribution question with
n = 5
p = 0.4
q = 1 - p = 0.6
where



Please hit thumps up if the answer helped you