Question

The distribution of the amount of money spent by first-time gamblers at a major casino in Las Vegas is approximately normal in shape with a mean of $600 and a standard deviation of $120. According to the standard deviation rule, almost 84% of gamblers spend more than what amount of money at this casino?

Answer 1

Answer:

amount of money  = 480

Explanation:

given data

mean = $600

standard deviation SD = $120

amblers spend  = 84%

solution

As here 84% values fall within ±1 SD of mean

so here 16% above = mean +1 × SD

and 16% below = mean -1 × SD  

so by standard deviation rule

about 84% more than = mean -1 × SD  

so here

amount of money = mean  -1 × SD  

amount of money = 600 - 1 × 120

amount of money  = 480

Answer 2

The amount of money spent by gamblers at the casino can be calculated with the use of formula of standard deviation, which is calculated down to as $480 by each gambler.

To calculate the amount of money spent by each gambler at the casino, we will put the given values to the formula of standard deviation and arrive at the solution.

Standard Deviation.

• It has been provided that the mean money spent by the gamblers at the casino in Las Vegas is $600 and the standard deviation has been given as $120.

• The formula for calculation of standard deviation is as below,

• $\rm Amount\ of\ Money\ Spent= Mean - 1\ x\ Standard\ Deviation$

• Now putting the values to the given formula, we get

• $\rm Amount\ of\ Money\ Spent= 600-1\ x\ 120\\\\\\\rm Amount\ of\ Money\ Spent=\ 480$  

• So we come to know that a first timer spends at least $480 at the casino.

Hence, as per the standard deviation rule, the first time casino player spends $480 at the Las Vegas casino when the mean is $600 and the standard deviation is 120.

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