Question

Delicious Candy markets a two-pound box of assorted chocolates. Because of imperfec- tions in the candy making equipment, the actual weight of the chocolate has a uniform distribution ranging from 31 to 32.5 ounces. What is the probability that a box weighs less than 31.8 ounces?

Answer 1

Answer:

The required probability is 0.533.

Step-by-step explanation:

Consider the provided information.

The actual weight of the chocolate has a uniform distribution ranging from 31 to 32.5 ounces.

Let x is the random variable for the actual weight of chocolate.

According to PDF function.

$P(a\leq x\leq b)=\int\limits^b_a {f(x)} \, dx$

Where $f(x)=\left\{\begin{matrix}\frac{1}{b-a} & a<x<b\\ 0 & otherwise \end{matrix}\right.$

It is given that ranging from 31 to 32.5 ounces.

Substitute a=31 and b=32.5 in above function.

$f(x)=\left\{\begin{matrix}\frac{1}{32.5-31} & 31<x<32.5\\ 0 & otherwise \end{matrix}\right.$

$f(x)=\left\{\begin{matrix}\frac{1}{1.5} & 31<x<32.5\\ 0 & otherwise \end{matrix}\right.$

We need to find the probability that a box weighs less than 31.8 ounces

Now according to PDF:

$P(x<31.8)=\int\limits^{31.8}_{31} {\frac{1}{1.5} \, dx$

$P(x<31.8)=\frac{1}{1.5}[31.8-31]\\P(x<31.8)=\frac{0.8}{1.5}\\P(x<31.8)=0.533$

Hence, the required probability is 0.533.