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QuestionCalculate the mean of Ashley's friends' expenses: \$ 2,800, \$ 1,990, \$ 2,005, \$ 2,400, \$ 1,860, \$ 2,200, \$ 2,000. Is it higher or lower than \$ 2,110? What must Ashley spend for the average to be \$ 2,110?

Studdy Solution

STEP 1

Assumptions1. The estimated average discretionary personal expenses for a school year is ,110.Ashleypolledsevenofherfriends,andtheiractualschool−yearexpenseswere,110. Ashley polled seven of her friends, and their actual school-year expenses were ,800, 1,990,1,990, ,005, ,400,,400, 1,860, ,200,,200, ,0003. We are asked to find the mean of her friends' personal expenses, compare it with the estimated average, and find out what Ashley's actual personal expenses for that school year would have to be so that her amount and her friends' amounts together would have an average of $,110

STEP 2

First, we need to find the mean of her friends' personal expenses. The mean is calculated by adding up all the values and then dividing by the number of values.
Mean=Sum of valuesNumber of valuesMean = \frac{Sum\, of\, values}{Number\, of\, values}

STEP 3

Now, plug in the given values for the personal expenses of Ashley's friends to calculate the sum.
Sum of values=$2,800+$1,990+$2,005+$2,400+$1,860+$2,200+$2,000Sum\, of\, values = \$2,800 + \$1,990 + \$2,005 + \$2,400 + \$1,860 + \$2,200 + \$2,000

STEP 4

Calculate the sum of the values.
Sum of values=$2,800+$1,990+$2,005+$2,400+$1,860+$2,200+$2,000=$15,255Sum\, of\, values = \$2,800 + \$1,990 + \$2,005 + \$2,400 + \$1,860 + \$2,200 + \$2,000 = \$15,255

STEP 5

Now that we have the sum of the values, we can divide this by the number of values (7) to find the mean.
Mean=Sum of valuesNumber of values=$15,2557Mean = \frac{Sum\, of\, values}{Number\, of\, values} = \frac{\$15,255}{7}

STEP 6

Calculate the mean of her friends' personal expenses.
Mean=$15,255=$2,179.29Mean = \frac{\$15,255}{} = \$2,179.29a. The mean of her friends' personal expenses is $2,179.29.

STEP 7

Now, we need to compare the mean of her friends' personal expenses with the estimated average. If the mean is higher than the estimate, then the average is higher. If the mean is lower than the estimate, then the average is lower.
b. The mean of her friends' personal expenses (2,179.29)ishigherthantheestimatedaverage(2,179.29) is higher than the estimated average (2,110). Therefore, the average is higher.

STEP 8

Now, we need to find out what Ashley's actual personal expenses for that school year would have to be so that her amount and her friends' amounts together would have an average of 2,110.Theformulatofindtheaverageis2,110. The formula to find the average isAverage=Sum of values+Ashley′s expensesNumber of values+1Average = \frac{Sum\, of\, values + Ashley's\, expenses}{Number\, of\, values +1}$

STEP 9

Now, plug in the given values for the sum of values, number of values, and the average to calculate Ashley's expenses.
$2,110=$15,255+Ashley′s expenses7+\$2,110 = \frac{\$15,255 + Ashley's\, expenses}{7 +}

STEP 10

olve the equation for Ashley's expenses.
Ashley′s expenses=$2,110times8−$15,255Ashley's\, expenses = \$2,110 \\times8 - \$15,255

STEP 11

Calculate Ashley's actual personal expenses for that school year.
Ashley′s expenses=$,110times8−$15,255=$,325Ashley's\, expenses = \$,110 \\times8 - \$15,255 = \$,325c. Ashley's actual personal expenses for that school year would have to be ,325sothatheramountandherfriends′amountstogetherwouldhaveanaverageof,325 so that her amount and her friends' amounts together would have an average of ,110.

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