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25 May, 13:15

A casino knows that people play slot machines in hopes of hitting the jackpot but that most of them lose their dollar. Suppose that a certain slot machine pays out an average of $0.95 with a standard deviation of $105. a) Why is the standard deviation so large? b) If the machine is played 5 times, what are the mean and standard deviation of the casino's profit? c) If gamblers play this machine 1000 times in a day, what are the mean and standard deviation of the casino's profit? d) Is the casino likely to be profitable?

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  1. 25 May, 15:22
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    A) Gamblers lose a relatively small amount most of the time but there are a few large pay-outs

    B) if person play 5 times, the mean of the casino's profit is $0.04

    if person play 5 times, the standard deviation of the casino's profit i$268.33

    C) If gamblers play this machine 1000 times in a day, the mean is $80

    If gamblers play this machine 1000 times in a day, the standard deviation is $3794.3

    D) Yes

    Step-by-step explanation:

    From the details given, it is observed that a casino knows that people play the soft machines in hopes of hitting the jackpot but most of them lose their dollars

    There is a certain machine that pays out an average of $0.92 with standard deviation of $120

    A) The standard deviation is so large because, Gamblers lose a relatively small amount most of the time but there are a few large pay-outs

    B) if person play 5 times, the mean of the casino's profit is

    E (x) = (1 - $0.92) x 5

    = $0.04

    if person play 5 times, the standard deviation of the casino's profit is

    S (3x) = √120² x 5

    = $268.33

    C) If gamblers play this machine 1000 times in a day, the mean is

    E (x) = (1 - $0.92) x 1000

    = $80

    If gamblers play this machine 1000 times in a day, the standard deviation is

    S (x) = √120² x 1000

    = $3794.3

    D) The casino is likely to be profitable due to the average pays out winning jackpot in slot machines occur very less in $0.29, so more people play winning jackpot in slot machines in casino, the casino will become more profitable.
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