Question

The manager of a pizza chain in Albuquerque, New Mexico, wants to determine the average size of their advertised 14-inch pizzas. She takes a random sample of 35 pizzas and records their mean and standard deviation as 14.30 inches and 1.30 inches, respectively. She subsequently computes the 99th percentile of the sample. What is the value of the 99th percentile?

Answer 1

The value of the 99th percentile for the advertised 14-inch pizzas is approximately 15.898 inches.

Step-by-step explanation:

In statistical terms, the 99th percentile is the value below which 99% of the data falls. To calculate this for the pizza sizes, we use the standard normal distribution, also known as the Z-distribution. The formula for finding the Z-score is (X - μ) / σ, where X is the observed value, μ is the mean, and σ is the standard deviation.

In this case, the mean (μ) is given as 14.30 inches, and the standard deviation (σ) is 1.30 inches. To find the Z-score corresponding to the 99th percentile, we refer to a standard normal distribution table or use statistical software. The Z-score for the 99th percentile is approximately 2.33.

Now, we use the inverse Z-score formula to find the actual size corresponding to this Z-score: X = μ + Zσ. Plugging in the values, we get X = 14.30 + (2.33 * 1.30), which results in approximately 15.898 inches. Therefore, the value of the 99th percentile for the advertised 14-inch pizzas is approximately 15.898 inches, meaning that 99% of the sampled pizzas have a size of 15.898 inches or smaller.

This calculation is crucial for the pizza chain manager to ensure that their advertised 14-inch pizzas meet customer expectations consistently, helping maintain customer satisfaction and the reputation of the pizza chain.