Dee's store monthly sales for April, May, June are three independent random variables with means and variances as follow:

April:
Mean: $9500
Variance: $1250

May:
Mean: $7400
Variance: $1425

June:
Mean: $8600
Variance: $1610

a) find the mean and standard deviation of the total sales for the 2nd quarter (3 month period).

-I don't understand, what is the 2nd quarter??

b) If the store manager is paid by a base monthly salary of $2000 plus 10% of the monthly sales as commission, what is the mean and standard deviation of his monthly salary for May?

Dee's store monthly sales for April, May, June are three independent random variables with means and variances as follow:

April:
Mean: $9500
Variance: $1250

May:
Mean: $7400
Variance: $1425

June:
Mean: $8600
Variance: $1610

a) find the mean and standard deviation of the total sales for the 2nd quarter (3 month period).

-I don't understand, what is the 2nd quarter??

b) If the store manager is paid by a base monthly salary of $2000 plus 10% of the monthly sales as commission, what is the mean and standard deviation of his monthly salary for May?

2nd quarter probably implies the three months at hand (April, May, June). 1st quarter would have been Jan, Feb, March.

ok, i see, then i think i know how to do a), but i need some help on b).

Sure, I can help you with that!

For part a), to find the mean of the total sales for the 2nd quarter, you simply need to add up the means of each month. So the mean of the total sales for the 2nd quarter is:

Mean = Mean of April + Mean of May + Mean of June

Mean = $9500 + $7400 + $8600

To find the standard deviation of the total sales for the 2nd quarter, you need to consider that the sales for each month are independent variables. Since variances add up for independent variables, the variance of the total sales for the 2nd quarter is:

Variance = Variance of April + Variance of May + Variance of June

Variance = $1250 + $1425 + $1610

Once you have the variance, you can calculate the standard deviation by taking the square root of the variance.

Now let's move on to part b), where you need to find the mean and standard deviation of the store manager's monthly salary for May. The salary depends on both the base monthly salary of $2000 and the commission, which is 10% of the monthly sales.

To find the mean of the monthly salary for May, you need to calculate the commission on the mean sales for May and add it to the base monthly salary:

Mean Salary = Base Monthly Salary + (Commission Rate * Mean Sales)

Mean Salary = $2000 + (0.1 * Mean of May)

To find the standard deviation of the monthly salary for May, you need to consider that the commission is a percentage of the sales, and the sales for May are an independent variable with its own variance. So the variance of the monthly salary for May is:

Variance = (Commission Rate * Mean Sales)^2 * Variance of May

To get the standard deviation, you can take the square root of the variance.

I hope that helps! Let me know if you need any further clarification.