Help with normal distribution

Daily sales in a store follows a normal distribution with mean $2000 and standard deviation $500. Suppose daily sales are independent from day to day.

a) In the next 3 days, the probability that daily sales exceed $2000 in at least two days is ______.

b) In the next 9 days, the probability that the average daily sales is over $1800 is ______.

Re: Help with normal distribution

Hey alb41192.

The sum of independent normal distributions are normally distributed with the means added up and the variances added up.

So for three days you have a mean of 3*mu and a variance of 3*sigma^2.

This means you are looking at Z ~ (X - 3*mu)/SQRT(3*sigma^2).

Now this is for X1 = 3Y where this is for three days. If you want to do this for two days then you need to use X2 = 2Y.

The probabilities are P(X1 > 2000 OR X3 > 2000) and P(X_bar > 1800).

Recall that X_bar is equal to (X1 + X2 + ... + XN)/n which has mean mu and variance sigma^2/n.