A cement truck delivers mixed cement to a large construction site. Let x represe
ID: 3129451 • Letter: A
Question
A cement truck delivers mixed cement to a large construction site. Let x represent the cycle time in minutes for the truck to leave the construction site, go back to the cement plant, fill up, and return to the construction site with another load of cement. From past experience, it is known that the mean cycle time is mu = 42 minutes with sigma = 16 minutes. The x distribution is approximately normal. (a) What is the probability that the cycle time will exceed 60 minutes, given that it has exceeded SO minutes? (Round your answer to four decimal places.) (b) What is the probability that the cycle time will exceed 55 minutes, given that it has exceeded 40 minutes? (Round your answer to four decimal places.)Explanation / Answer
a)
We first get the z score for the critical value. As z = (x - u) / s, then as
x = critical value = 50
u = mean = 42
s = standard deviation = 16
Thus,
z = (x - u) / s = 0.5
Thus, using a table/technology, the right tailed area of this is
P(z > 0.5 ) = 0.308537539
***
We first get the z score for the critical value. As z = (x - u) / s, then as
x = critical value = 60
u = mean = 42
s = standard deviation = 16
Thus,
z = (x - u) / s = 1.125
Thus, using a table/technology, the right tailed area of this is
P(z > 1.125 ) = 0.130294517
****
Hence,
P(x>60|x>50) = 0.130294517/0.308537539 = 0.422297129 [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 = 40
u = mean = 42
s = standard deviation = 16
Thus,
z = (x - u) / s = -0.125
Thus, using a table/technology, the right tailed area of this is
P(z > -0.125 ) = 0.549738225
***
We first get the z score for the critical value. As z = (x - u) / s, then as
x = critical value = 55
u = mean = 42
s = standard deviation = 16
Thus,
z = (x - u) / s = 0.8125
Thus, using a table/technology, the right tailed area of this is
P(z > 0.8125 ) = 0.208252393
Hence,
P(x>55|x>40) = 0.208252393/0.549738225 = 0.378821016 [ANSWER]
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