Two college roommates have each committed to donating to charity each week for the next year. the roommates’ weekly incomes are independent of each other. suppose the amount donated in a week by one roommate is approximately normal with mean $30 and standard deviation $10, and the amount donated in a week by the other roommate is approximately normal with mean $60 and standard deviation $20. which of the following is closest to the expected number of weeks in a 52-week year that their combined donation will exceed $120 ? 0; the combined donation never exceeds $120 in a weeka1 weekb3 weeksc5 weeksd8 weeks

C. 5 weeks.

Step-by-step explanation:

In this question we have a random variable that is equal to the sum of two normal-distributed random variables.

If we have two random variables X and Y, both normally distributed, the sum will have this properties:

To calculate the expected weeks that the donation exceeds $120, first we can calculate the probability of S>120:

The expected weeks can be calculated as the product of the number of weeks in the year (52) and this probability:

The nearest answer is C. 5 weeks.

The expected number of weeks can be calculated by finding the probability. To find the probability, we have random variable that is equal to the sum of two normal-distributed random variables.

The correct answer is 5 weeks (c).

Given:

Normal distribution is and .

Standard deviation is and .

Calculate the normal distribution.

Calculate the standard deviation.

Calculate the probability of .

So,

Calculate the expected week.

Thus, the correct answer is 5 weeks (c).

Learn more about what normal-distributed random variables is here:

link

0.02

step-by-step explanation:

time of 9 192 631 770 periods of the radiation corresponding to the transition between the 2 hyperfine levels of the ground state of the caesium 133 atom at 0 k (but other seconds are sometimes used in astronomy)