Question

a vending machine dispenses coffee into an 8 oz cup. the amount of coffee dispensed into the cup is normally distributed with a standard deviation of 0.03 oz.you can allow the cup to overfill 1 percent of the time. what among should you set as the mean amount of coffee to be dispensed?

Answer 1

Using a normal distribution function, select the value of x(mean) that makes the probability integral of P(x) from x = 0 to 8.0 equal to 0.99, when sigma = 0.03

Answer 2

You may find the JAVA tool at this website for problems of this type.
http://psych-www.colorado.edu/~mcclella/java/normal/accurateNormal.html
I used it to get an answer of 7.93 oz.
Enter mean of 7.93, sigma = 0.03 and the range of P(x) 0 to 8.0 oz, and you get a probability of 0.990

Answer 3

Use Norminv in excel(%, cup size, stanard dev ) then round to the 2nd decimal

hope this helpful

Answer 4

Find the z-value with a right tail of 1%: z = 2.3263
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Find the x-value using x = zs+u
x = 2.3263*0.01+8 = 8.0233
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Let that be the mean amount of coffee to be dispensed