the age of costumers for a particular retail store follows a normal distribution with a mean of 37.5 years and a standard deviation of 7.6 years. what is the probability that the next costumer who enters the store will be less than 42 years old?
z= (42-37.5)/7.6
z = 0.59
Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion/probability related to the Z score.
To find the probability that the next customer who enters the store will be less than 42 years old, we can use the properties of the normal distribution.
Step 1: Standardize the value
To use the normal distribution table, we need to standardize the value of 42 years to a z-score. Z-score represents the number of standard deviations the value is away from the mean. We can calculate the z-score using the formula:
z = (x - μ) / σ
Where:
x = Value we want to standardize (42 years)
μ = Mean of the distribution (37.5 years)
σ = Standard deviation of the distribution (7.6 years)
z = (42 - 37.5) / 7.6
z = 4.5 / 7.6
z = 0.5921
Step 2: Look up the z-score
Using a standard normal distribution table (also known as the z-table or a statistical software), we can find the corresponding area under the curve for the z-score of 0.5921. The area represents the probability that a randomly selected customer will be less than 42 years old.
Looking up the z-score in the table, we find that the area is approximately 0.7241. This means that the probability that the next customer who enters the store will be less than 42 years old is about 0.7241 or 72.41%.
So, the probability is 0.7241 or 72.41%.