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
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.