QuestionFind the average mass of pennies with $12\%$ from San Francisco ( $2.2 \mathrm{~g}$ ) and $88\%$ from Philly ( $2.156 \mathrm{~g}$ ).

Studdy Solution

STEP 1

Assumptions1. The percentage of pennies minted in San Francisco is12.00% . The average mass of pennies minted in San Francisco is. g3. The percentage of pennies minted in Philly is88.00%
4. The average mass of pennies minted in Philly is.156 g5. We are looking for the overall average mass of the pennies in the sample

STEP 2

We can calculate the average mass of the pennies in the sample by taking a weighted average. The weight of each group of pennies is proportional to its percentage in the total sample.
$Average\, mass = (Percentage\, of\, SF\, pennies \\times Average\, mass\, of\, SF\, pennies) + (Percentage\, of\, Philly\, pennies \\times Average\, mass\, of\, Philly\, pennies)$

STEP 3

Now, plug in the given values for the percentages and average masses to calculate the average mass.
$Average\, mass = (12.00\% \\times2.2\, g) + (88.00\% \\times2.156\, g)$

STEP 4

Convert the percentages to decimal values.
$12.00\% =0.12$ $88.00\% =0.88$ $Average\, mass = (0.12 \\times2.2\, g) + (0.88 \\times2.156\, g)$

STEP 5

Calculate the average mass.
$Average\, mass = (0.12 \\times2.2\, g) + (0.88 \\times2.156\, g) =2.1652\, g$ The average mass of pennies in this sample is2.1652 g.

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