Making handcrafted pottery generally takes two major steps: wheel throwing and f
ID: 3133828 • Letter: M
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 and 3 min, respectively. (Please note that wheel throwing and firing are independent.) Round your answers to four decimal places (e.g. 98.7654). What is the probability that a piece of pottery will be finished within 100 min? What is the probability that it will take longer than 110 min?Explanation / Answer
The mean making time is then
u(A+B) = u(A) + u(B) = 40 + 60 = 100
and standard deviation of
sigma(A+B) = sqrt(sigma^2(A) + sigma^2(B)) = sqrt(2^2 + 3^2) = 3.605551275
a)
We first get the z score for the critical value. As z = (x - u) / s, then as
x = critical value = 100
u = mean = 100
s = standard deviation = 3.605551275
Thus,
z = (x - u) / s = 0
Thus, using a table/technology, the left tailed area of this is
P(z < 0 ) = 0.5 [ANSWER]
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b)
We first get the z score for the critical value. As z = (x - u) / s, then as
x = critical value = 110
u = mean = 100
s = standard deviation = 3.605551275
Thus,
z = (x - u) / s = 2.773500981
Thus, using a table/technology, the right tailed area of this is
P(z > 2.773500981 ) = 0.002772834 [ANSWER]
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