#14 Vending Machines Quarters are now manufactured so that they have a mean weig
ID: 3360463 • Letter: #
Question
#14 Vending Machines Quarters are now manufactured so that they have a mean weight of 5.670g and a standard deviation of 0.062g, and their weights are normally distributed. A vending machine is configured to accept only those quarters that weigh between 5.550g and 5.790g. a. If 1 randomly selected quarter is inserted into the vending machine, what is the probability that it will be accepted? b. If 4 randomly selected quarters are inserted into the vending machine, what is the probability that their mean weight is between 5.550g and 5.790g? c. If you own the vending machine, which result is more important: the result from part (a) or part (b)?Explanation / Answer
mean = 5.67
std. dev. = 0.062
a)
Probability that a randomly selected coin weighs betwwen 5.55 and 5.79
P(5.55 < X < 5.79)
= P((5.55 - 5.67)/0.062 < X < (5.79 - 5.67)/0.062)
= P(-1.9355 < z < 1.9355)
= P(z < 1.9355) - P(z < -1.9355)
= 0.9735 - 0.0265
= 0.9471
Hence probability that a coin will be accepted, p = 0.9471
b)
SE = 0.062/sqrt(4) = 0.031
P(5.55 < X < 5.79)
= P((5.55 - 5.67)/0.031 < X < (5.79 - 5.67)/0.031)
= P(-3.8709 < z < 3.8709)
= P(z < 3.8709) - P(z < -3.8709)
= 0.9999 - 0.000054
= 0.99989
c)
Results from part (a) more important
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