Shoppers were asked how much money they were going to spend today in the mall. The mean dollars was $250 with a standard deviation of $15. In a group of 64 people, what is the probability that they spent less than $240?

To calculate the probability that shoppers spent less than $240, we need to use the standard deviation, mean, and the concept of the normal distribution.

Step 1: Determine the z-score
The z-score measures the number of standard deviations a particular value is from the mean. It's calculated using the following formula:
z = (x - μ) / σ
where:
x = value (in this case, $240)
μ = mean ($250)
σ = standard deviation ($15)

Substituting the given values into the formula:
z = (240 - 250) / 15
z = -10 / 15
z = -0.67

Step 2: Look up the z-score
Find the corresponding probability of the z-score in the standard normal distribution table (also known as the Z-table). The z-table provides the probability of obtaining a value less than the z-score.

Step 3: Calculate the probability
Since we want to find the probability that shoppers spent less than $240, we need to find the area under the normal curve to the left of the z-score (-0.67).

Consulting the z-table, the probability corresponding to a z-score of -0.67 is approximately 0.2514.

Therefore, the probability that the group of 64 shoppers spent less than $240 is 0.2514 or 25.14%.