Question

the distribution of the number of transactions per day at a certain automated teller machine (atm) is approximately normal with a mean of 80 transactions and a standard deviation of 10 transactions. which of the following represents the parameters of the distribution?
(a) $\bar{x}=80; s = 10$
(b) $\bar{x}=80; s^{2}=10$
(c) $\bar{x}=80; sigma = 10$
(d) $mu=80; sigma = 10$
(e) $mu=80; s = 10$

Explanation:

Step1: Recall parameter notation

In a normal - distribution, the population mean is denoted by $\mu$ and the population standard deviation is denoted by $\sigma$. The sample mean is denoted by $\bar{x}$, the sample standard deviation by $s$, and the sample variance by $s^{2}$.

Step2: Identify given values as population parameters

We are given the mean and standard deviation of the distribution of the number of transactions per day at an ATM. Since these are characteristics of the entire distribution (not a sample), they are population parameters. The mean of the distribution is $\mu = 80$ and the standard deviation is $\sigma=10$.

Answer:

D. $\mu = 80;\ \sigma = 10$