Question

A hardware store sells lightbulbs in the following wattages: 25, 40, 60, 75, 100. At midday the store sells out of 75-watt bulbs. By how many watts does the mean decrease?(1 point)
Responses

5.1
5.1

3.7
3.7

60
60

56.3

Answer 1

To find out how the mean wattage of the lightbulbs decreases when the store sells out of 75-watt bulbs, we first calculate the mean wattage before and after selling out of the 75-watt bulbs.

Initially, the available wattages are: 25, 40, 60, 75, 100.

**Step 1: Calculate the initial mean wattage.**

Sum of wattages:
\[
25 + 40 + 60 + 75 + 100 = 300
\]

Number of wattages:
\[
5
\]

Mean wattage:
\[
\text{Mean} = \frac{\text{Sum of wattages}}{\text{Number of wattages}} = \frac{300}{5} = 60
\]

**Step 2: Calculate the mean wattage after selling out of 75-watt bulbs.**

Now the available wattages are: 25, 40, 60, 100.

Sum of remaining wattages:
\[
25 + 40 + 60 + 100 = 225
\]

Number of remaining wattages:
\[
4
\]

Mean wattage:
\[
\text{Mean} = \frac{225}{4} = 56.25
\]

**Step 3: Calculate the decrease in mean wattage.**

Original mean wattage:
\[
60
\]

New mean wattage:
\[
56.25
\]

Decrease in mean:
\[
60 - 56.25 = 3.75
\]

Considering the options given, none exactly match this value. The closest option is "3.7", which rounds to 3.75. Thus, the mean decrease in wattage is:

**3.7**