A business woman wants to open a coffee stand across the street from a competing coffee company. She notices that the competing company has an average of 170 customers each day, with a standard deviation of 45 customers. Suppose she takes a random sample of 31 days. Identify the following to help her decide whether to open her coffee stand, rounding to the nearest whole number when necessary: μ =customers per day
σ =customers per day
n =
μ-x =
σ-x =customers per day

μ = 170 customers per day

σ = 45 customers per day

n = 31

Step-by-step explanation:

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean and standard deviation , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean and standard deviation .

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

She notices that the competing company has an average of 170 customers each day, with a standard deviation of 45 customers.

This means that

Suppose she takes a random sample of 31 days.

This means that

For the sample:

By the Central Limit Theorem, the mean is and the standard deviation is