Making handcrafted pottery generally takes two major steps: wheel throwing and fi ring. The time of wheel throwing and the time of fi ring are normally distributed random variables with means of 40 minutes and 60 minutes and standard deviations of 2 minutes and 3 minutes, respectively.

(a) What is the probability that a piece of pottery will be finished within 95 minutes?

(b) What is the probability that it will take longer than 110 minutes?

Answer

Step 1 of 2</p>

(a)

We are asked to find the probability that a piece of pottery will be finished within

Let denote the total time.

Let denote wheel throwing.

Let denote wheel firing.

Then, ……….(1)

We need to find

If are independent, normal random variables

Then we can write,

…….(2)

………(3)

Hence the mean and standard deviation of the total time of wheel throwing and the time of firing using equation

……….(4)

Compare equation (1) and (4), we get

Since total time follows normal distribution, we can write,

Using table, the area to the left of is

Hence the probability that a piece of pottery will be finished within is