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# Making handcrafted pottery generally takes two major ISBN: 9781118539712 55

## Solution for problem 66E Chapter 5.4

Applied Statistics and Probability for Engineers | 6th Edition

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Problem 66E

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?

Step-by-Step Solution:

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 Step 2 of 2

##### ISBN: 9781118539712

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