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 notations

In a normal - distribution, the population mean is denoted by $\mu$ and the population standard deviation is denoted by $\sigma$. Sample mean is denoted by $\bar{x}$ and sample standard deviation is denoted by $s$. The problem is asking for parameters of the distribution, which refer to population - level values.

Step2: Identify the correct notation for mean and standard deviation

The mean of the distribution is 80 and the standard deviation is 10. For population parameters, the mean is $\mu$ and the standard deviation is $\sigma$. So the parameters of the distribution are $\mu = 80$ and $\sigma=10$.

Answer:

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