The gross weekly sales at a certain super market are a Gaussian random with mean $2200 and standard deviation $230. Assume that the sales from week to week are independent. A) Find the probability that the gross sales over the next two weeks exceed $5000.
B) Find the probability that the gross weekly sales exceed $2000 in at least 2 of the next 3 weeks.

A)  P(Z > 5000) = 0.0322

B)  P( Y = 2 or 3) ≅  0.9032

Step-by-step explanation:

From the given information;

Suppose the sales for the first week are denoted by X and the sales for the second week are denoted by Y.

Then;

X & Y are independent and they follow a normal distribution.

i.e.

If we set Z to be equal to X+Y

Then, since two normal distribution appears normal

So;

From the Z - tables;

P(Z > 5000) = 1 - 0.9678

P(Z > 5000) = 0.0322

B)

Let Y be the random variable that obeys the Binomial distribution.

Y represents the numbers of weeks in the next 3 weeks where the gross weekly sales exceed $2000

Thus;

where;

p = 1 - P( Z < - 0.869565)

From the Z - tables;

p = 1 - 0.1924

p = 0.8076

Now;

P(Y ≥ 2) = P(Y = 2) + P( Y =3 )

Using the formula

P( Y = 2 or 3) = 0.9031911541

P( Y = 2 or 3) ≅  0.9032

check above link.

graphically?   well, you graph them both, the solutions is where they both intersect each other, since there are two solutions, meaning they will meet twice, or namely the linear will run into the quadratic curve twice, and where they meet, those x,y coordinates are the solutions to the system.