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

cosine

step-by-step explanation: