Question

An ice cream shop's goal is to sell a mean of 45 ice cream cones per day. In one week, it sold the following numbers of Ice cream cones each day. 54, 45, 33, 39, 48, 40, 41How many more Ice cream cones would it have had to sell during the week to meet its goal?

Answer 1

Explanation

By definition, the mean value of a set of data with n elements x₁, ..., xₙ, is given by:

$m=\frac{x_1+x_2+...+x_n}{n}=\frac{S}{n}.$

We see that the numerator S is the sum of all the numbers in the set.

We know that the ice cream shop sold the following number of ice creams during the week: 54, 45, 33, 39, 48, 40, 41. The sum of these numbers is:

$S=54+45+33+39+48+40+41=300.$

The mean value for this quantity is:

$m=\frac{S}{n}=\frac{300}{7}\cong43.$

But for a mean value m' = 45 and n' = 7, we must have a sum:

$S^{\prime}=m^{\prime}\cdot n^{\prime}=45\cdot7=315.$

To have a mean value of 45, the shop must sell:

$S^{\prime}-S=315-300=15$

ice creams more.

Answer

D. 15