Question

In a large sample of customer accounts, a utility company determined that the average number of days between when a bill was sent out and when the payment was made is 42 with a standard deviation of 8 days. Assume the data to be approximately bell-shaped.1. Between what two values will approximately 95% of the numbers of days be?

Answer 1

Answer:

Approximately 95% of the numbers of days will be between 26 and 58.

Step-by-step explanation:

We are given the following in the question:

Mean, μ = 42

Standard Deviation, σ = 8

We are given that the distribution of average number of days between a bill is a bell shaped distribution that is a normal distribution.

Empirical Formula:

• According to Empirical formula almost all the data lies within three standard deviation of man for a normal distribution.
• Almost 68% of data lies within 1 standard deviation of mean.
• Almost 95% of data lies within two standard deviation of mean.
• Almost 99.7% of data lies within three standard deviation of mean.

Thus, by Empirical formula 95% of data lies within two standard deviation.

$\mu \pm 2(\sigma) \\=42 \pm 2(8)\\=42 \pm 16\\=(26, 58)$

Thus, approximately 95% of the numbers of days will be between 26 and 58.