After 1964, quarters were manufactured so that the weights had a mean of 5.67g w
ID: 3050651 • Letter: A
Question
After 1964, quarters were manufactured so that the weights had a mean of 5.67g with a standard deviation of 0.06g. Some vending machines are designed so that you can adjust the weights of quarters that are accepted. If many counterfeit coins are found, you can narrow the range of acceptable weights with the effect that most counterfeit coins rejected along with some legitimate quarters. a) if you adjust vending machines to accept weight between 5.64 and 5.70g, what percentage of legal quarters are rejected? b) If you adjust vending machines to accept the middle 95% of quarters, what weights of quarters will be rejected?
Explanation / Answer
a)
probability of acceptance:
hence percentage of legal quarters are rejected =(1-0.3829)*100 =61.71%
b)
for middle 95% lie between 2.5 and 97.5 percentile ;for which z score =1.96
hence corresponding limits =mean -/+ z*Std deviation =5.55 to 5.79
for normal distribution z score =(X-)/ here mean= = 5.670 std deviation == 0.06Related Questions
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