Making handcrafted pottery generally takes two major steps: wheel throwing and f

Question

Making handcrafted pottery generally takes two major steps: wheel throwing and firing. The time of wheel throwing and the time of firing are normally distributed random variables with means of 40 min and 60 min and Standard deviations of 2 min, respectively. Throwing and firing are independent. What is the probability that a piece of pottery will be finished between 80 and 95 min? Show your work and place a box around your final answer. Determine the MGF of the Bernoulli distribution. Show your work and place a box around your final answer.

Explanation / Answer

Question 1:

We need to find the combined mean and standard deviations:

Mean = 40 + 60 = 100

Standard deviation = Ö[2^2 + 3^2] = Ö13 = 3.6056

We need to find the below probability:

P (80 < x < 95)

z = (x – Mean) / Standard deviation

The z-score for 80 = (80-100)/ 3.6056 = -5.55

The z-score for 95 = (95 – 100)/ 3.6056 = -1.39

P (-5.55 < z < -1.39)

= P (z < -1.39) – P (z < -5.55)

= 0.0823 – 0.0000

=0.0823

Answer: 0.0823

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