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pogonyaev
3 years ago
14

A vending machine operator has determined that the number of candy bars sold per week by a certain machine is a random variable

with mean 125 and standard deviation 7. His profit on each bar sold is $0.25, and it costs him $2.00 per day to maintain the machine and rent the space for it. What is the mean for Y
Mathematics
1 answer:
docker41 [41]3 years ago
6 0

Answer:

The answer is below

Step-by-step explanation:

Let Y represent the profit per day, and x represent the number of bar sold per day. Hence:

Y = 0.25x - 2

a) The mean is given as:

\mu_y=E(Y)=E(0.25X-2) = 0.25E(X)-2\\\\But\ E(X)=mean\ of\ machine=125. Hence:\\\\E(Y)=0.25(125)-2=29.25\\\\E(Y)=\$29.25

b) The standard deviation of y is:

\sigma_y=var(0.25X-2)\\\\\sigma_y=0.25\sigma(X)\\\\but\ \sigma_X=7,hence:\\\\\sigma_y=0.25(7)=1.75\\\\\sigma_y=\$1.75

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