Kara works at a jewlery store and earns commission on her total sales for the week. Her weekly paycheck was in the amount of $6,500, including her salary of $1,000. Her sales for the week totaled $45,000. Express her rate of commition as a percent, rounded to the nearest whole number

Her total paycheck minus her salary = the commission amount

So

6500 - 1000 = 5500

Soher commission as a percentage of sales = 5500/ 45000 = about 12.2%

A) Between 388 and 450

B) Between 357 and 481

C) Between 326 and 512

D) 99.995%

E) 72.907%

Step-by-step explanation:

We are given;

Mean; x¯ = 419 minutes

Standard deviation; σ = 31 minutes

A) From the empirical rule, 68% falls within 1 standard deviation.

Thus, it will be between;

419 - 1(31) and 419 + 1(31)

Thus gives;

Between 388 and 450

B) From the empirical rule, 95% falls within 2 standard deviation.

Thus, it will be between;

419 - 2(31) and 419 + 2(31)

Thus gives;

Between 357 and 481

C) From the empirical rule, 99.7% falls within 2 standard deviations.

Thus, it will be between;

419 - 3(31) and 419 + 3(31)

Thus;

Between 326 and 512

D)between 359 and 479 minutes, we will use z-s roe formula;

z = (479 - 359)/31

z = 3.871

From the z-table attached, we see that the probability is 0.99995 and as such, the percentage is 99.995%

E) worker spent 400 minutes on the job.

Thus;

z = (419 - 400)/31

z = 0.613

From z-tables, p = 0.72907

In percentage, we have; 72.907%