PROBLEMS TO HAND IN The Sands Casino did an audit of all of their dollar slot ma

Question

PROBLEMS TO HAND IN The Sands Casino did an audit of all of their dollar slot machines and found that the amount of money collected per night by a certain machine has a mean of $5000, a standard deviation of $100, and is approximately normally distributed. a) What is the probability that this machine will collect less than $5000 tomorrow night? c) What is the probability that this machine will collect less than $4700 tomorrow night? The casino would like to know when this machine has a "bad night" as defined by What is the probability that this machine will collect between $4900 and $5100 tomorrow night? b) d) What is the probability that this machine will collect between $5100 and $5200 tomorrow night? e) collecting less money than it collects in the top 84% of other nights. How much money must the machine make tomorrow to be considered not having a bad night?

Explanation / Answer

Formula: Z = (X - mean)/std. dev.

a) P(X < 5000) = P(Z < (5000 - 5000)/100) = 0.5 (using symmetry of normal distribution)

b) P(4900 < X < 5100), The data lies withn 1 standard deviation from the mean, therefore 68% or 0.68 of the total data lies betwenn 4900 and 5100.
Answer: 0.68 (Using 68 95 99.7% rule)

c) P(X < 4700), Less than 4700 is less than 3 standard deviations. Answer: (1- 0.997)/2 = 0.0015

d) P(5100 < X < 5200), This is the probability beween 1 and 2 standard deviations from the mean.

Answer: 0.975 - 0.84 = 0.135

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