Vending machines can be adjusted to reject coins above and below certain weights. The weights of legal U.S. quarters have a normal distribution with a mean of 5.67 grams and a standard deviation of 0.07 gram. If a vending machine is adjusted to reject quarters that weigh more than 5.81 grams and less than 5.53 grams, what percentage of legal quarters will be rejected by the vending machine

Question

13-04-2021
Mathematics

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Vending machines can be adjusted to reject coins above and below certain weights. The weights of legal U.S. quarters have a normal distribution with a mean of 5.67 grams and a standard deviation of 0.07 gram. If a vending machine is adjusted to reject quarters that weigh more than 5.81 grams and less than 5.53 grams, what percentage of legal quarters will be rejected by the vending machine

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JeanaShupp JeanaShupp · Answer 1 · 2021-04-17T10:46:24+02:00

Answer: The percentage of legal quarters will be rejected by the vending machine = 2.275%

Step-by-step explanation:

Given: The weights of legal U.S. quarters have a normal distribution with a mean of 5.67 grams and a standard deviation of 0.07 gram.

Let x be the weights of legal U.S. quarters .

Required probability: [tex]P(x<5.53)+P(x>5.81)[/tex]

[tex]=P(\dfrac{x-\mu}{\sigma}<\dfrac{5.33-5.67}{0.07})+P(\dfrac{x-\mu}{\sigma}>\dfrac{5.81-5.67}{0.07})\\\\=P(z<-4.857)+P(z>2)\approx0.02275 \ \ \ [By\ P-value\ calculator][/tex]

The percentage of legal quarters will be rejected by the vending machine = 2.275%