A popular retail store knows that the purchase amounts by its customers is a random variable that follows a normal distribution with a mean of $30 and a standard deviation of $9.

What is the probability that a randomly selected customer will spend $20 or more at this store?

To find the probability that a randomly selected customer will spend $20 or more at the store, we need to calculate the area under the normal distribution curve to the right of $20.

Step 1: Standardize the value of $20
The first step is to standardize the value of $20 using the formula: Z = (X - μ) / σ, where X is the value of interest, μ is the mean, and σ is the standard deviation.

In this case, X = $20, μ = $30, and σ = $9.

Using the formula, we get:
Z = (20 - 30) / 9 = -1.11

Step 2: Find the area to the right of Z = -1.11
To find the area to the right of Z = -1.11, we can use a standard normal distribution table (also known as the Z-table) or a statistical calculator.

Using a Z-table, locate the row that starts with -1.1 and the column that indicates 0.01. The intersection of this row and column will give us the area to the right of Z = -1.11.

The area in the table is 0.1335.

However, we need to consider that we're looking for the area to the right of Z = -1.11, so we subtract 0.1335 from 1 to get the final probability:

Probability = 1 - 0.1335 = 0.8665

Therefore, the probability that a randomly selected customer will spend $20 or more at this store is approximately 0.8665 or 86.65%.

Use z-scores:

z = (x - mean)/sd

With your data:

z = (20 - 30)/9 = ?

Finish the calculation. Next, look at a z-table to determine your probability. (Remember that the problem is asking "$20 or more" when looking at the table.)

I'll let you take it from here.