the monthly sales at a computer store have mean of $25,000 and a standard deviation of $4,000. profits are calculated by multiplying sales ny 30% and subtracting fixed cost of $60,000. find the mean and standard deviation of monthly profit
mean of the profit = 29000.its standard deviation = 9000
2900000
To find the mean and standard deviation of monthly profit, we will use the formula for calculating the mean and standard deviation of a function of a random variable.
Mean of Monthly Profit:
Step 1: Multiply the mean of the sales by 30% to calculate the mean of the profits:
Mean of Sales = $25,000
Mean of Profits = Mean of Sales * 30% = $25,000 * 0.30 = $7,500
Step 2: Subtract the fixed cost of $60,000 from the mean of the profits:
Mean of Monthly Profit = Mean of Profits - Fixed Cost = $7,500 - $60,000 = -$52,500
Therefore, the mean of the monthly profit is -$52,500.
Standard Deviation of Monthly Profit:
Step 3: Multiply the standard deviation of the sales by 30% to calculate the standard deviation of the profits:
Standard Deviation of Sales = $4,000
Standard Deviation of Profits = Standard Deviation of Sales * 30% = $4,000 * 0.30 = $1,200
Therefore, the standard deviation of the monthly profit is $1,200.
To find the mean and standard deviation of monthly profit, we can utilize the given mean and standard deviation of the monthly sales.
First, let's calculate the mean of the monthly profit. The profit is calculated by multiplying the sales by 30% and subtracting the fixed cost of $60,000. So, the mean profit can be calculated as:
Mean Profit = Mean Sales * 30% - Fixed Cost
Mean Profit = $25,000 * 0.3 - $60,000
Mean Profit = $7,500 - $60,000
Mean Profit = -$52,500
Therefore, the mean profit is -$52,500.
Next, let's calculate the standard deviation of the monthly profit. The standard deviation is determined by the variability in the sales, which is then translated to the profit. Since the profit is calculated based on sales, we can use the following formula:
Standard Deviation Profit = Standard Deviation Sales * 30%
Standard Deviation Profit = $4,000 * 0.3
Standard Deviation Profit = $1,200
Therefore, the standard deviation of the monthly profit is $1,200.