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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?

User Richard T
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3 votes

Answer:

The required probability is 0.533.

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}(1)/(b-a) &amp; a<x<b\\ 0 &amp; 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}(1)/(32.5-31) &amp; 31<x<32.5\\ 0 &amp; otherwise \end{matrix}\right.


f(x)=\left\{\begin{matrix}(1)/(1.5) &amp; 31<x<32.5\\ 0 &amp; 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) {(1)/(1.5) \, dx


P(x<31.8)=(1)/(1.5)[31.8-31]\\P(x<31.8)=(0.8)/(1.5)\\P(x<31.8)=0.533

Hence, the required probability is 0.533.

User Ilevent
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