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?

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.