Question

The cost of unleaded gasoline in the Bay Area once followed an unknown distribution with a mean of $\backslash (4.59$and a standard deviation of $\backslash )0.10$. Sixteen gas stations from the Bay Area are randomly chosen. We are interested in the average cost of gasoline for the $16$gas stations. The distribution to use for the average cost of gasoline for the $16$gas stations is:

a.$\overline{X}~N(4.59,0.10)$

b.$\overline{X}~N\left(4.59,\frac{0.10}{\sqrt{16}}\right)$

c.$\overline{X}~N\left(4.59,\frac{16}{0.10}\right)$

d.$\overline{X}~N\left(4.59,\frac{\sqrt{16}}{0.10}\right)$

Short answer

b.$\overline{X}~N\left(4.59,\frac{0.10}{\sqrt{16}}\right)$

Step-by-step solution

Given information

The cost of unleaded gasoline in the Bay Area once followed an unknown distribution with a mean of $\$4.59$and a standard deviation of $\$0.10$. Sixteen gas stations from the Bay Area are randomly chosen. We are interested in the average cost of gasoline for the $16$gas stations.

Explanation

the mean random variable is given by, $\overline{X}~N\left(\mu ,\frac{\sigma }{\sqrt{n}}\right)$

Plugging all the values in the above equation, we get

$\overline{X}~N\left(4.59,\frac{0.10}{\sqrt{16}}\right)$