The age of customers for a particular retail store follows a normal distribution with a mean of 37.5 years and a standard deviation of7.6 years.What is the probability that the next customer who enters the store will be less than 42 years old?
Z = (score-mean)/SD
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 need to calculate the area under the normal distribution curve up to the value of 42.
First, we need to standardize the value 42 using the z-score formula:
z = (x - μ) / σ
Where:
x = 42 (the value we want to find the probability for)
μ = 37.5 (mean)
σ = 7.6 (standard deviation)
Calculating the z-score:
z = (42 - 37.5) / 7.6
z ≈ 0.592
Once we have the z-score, we can use a standard normal distribution table (also known as the Z-table) or statistical software to find the corresponding probability.
Looking up the z-score of 0.592 in the standard normal distribution table, we find that the probability associated with this z-score is approximately 0.724
Therefore, the probability that the next customer who enters the store will be less than 42 years old is approximately 0.724, or 72.4%.