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

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