Quarters with weights have a normally distributed with a mean of 5.670 g and a s
ID: 3261762 • Letter: Q
Question
Quarters with weights have a normally distributed with a mean of 5.670 g and a standard deviation of 0.062 g. If a vending machine is configured to accept only those quarters with weights between 5.550 g and 5.790 g.
(Show all your work, including all the steps you have to do for each part to arrive at the correct answer.)
A) If 280 different quarters are inserted into the vending machine, what is the expected number of rejected quarters?
B) Find the IQR of the weights of the quarters in that particular vending machine?
Explanation / Answer
a) = 5.670;= 0.062;n = 280a.P(5.550 x 5.790)
= P[(5.550 – 5.670)/0.062] [(X – 5.670)/0.062] [(5.790 – 5.670/0.062]
= (1.935 Z 1.935)
= 0.9735 – 0.0265
= 0.94701.280(1 - 0.9470)
= 280(0.0530)
=14.84
= 15
Quarters a.If 280 different quarters are insertedinto the vending machine, the expected number of rejected quarters is 15.