Question

1. in their brochure, autonation career school estimated the average discretionary personal expenses for a student attending to be $2,850. martin is a student and feels that the amount is too high. he polled his co - students and made a list of their actual school year expenses: $2,500 $2,600 $3,000 $3,200 $2,700 $2,900 $2,850 a. what is the mean of these students’ personal expenses? round your answer to the nearest cent. b. how does that average compare with the estimate? c. what would martin’s actual personal expenses for that school year have to be so that his amount and his co - students’ amounts together would have an average of $2,850?

Explanation:

Step1: Calcular la suma de los gastos

$$\begin{align*} 2500 + 2600+3000 + 3200+2700+2900+2850&=(2500+2600)+(3000 + 3200)+(2700+2900)+2850\\ &=5100+6200+5600+2850\\ &=(5100+6200)+(5600+2850)\\ &=11300+8450\\ &=19750 \end{align*}$$

Step2: Calcular el promedio

El número de datos \(n = 7\). El promedio \(\bar{x}=\frac{\text{Suma de datos}}{n}\), entonces \(\bar{x}=\frac{19750}{7}\approx2821.43\)

Step3: Comparar el promedio con la estimación

La estimación es de \(2850\) y el promedio calculado es \(2821.43\). \(2821.43<2850\)

Step4: Calcular el gasto de Martin para un promedio de \(2850\)

Si el número de datos es \(n = 8\) (7 co - estudiantes + Martin) y el promedio \(\bar{x}=2850\), la suma total de los gastos debería ser \(S = n\times\bar{x}=8\times2850 = 22800\). La suma de los gastos de los 7 co - estudiantes es \(19750\). Entonces, los gastos de Martin \(x=22800 - 19750=3050\)

Answer:

a. \(2821.43\)
b. El promedio calculado (\(2821.43\)) es menor que la estimación (\(2850\))
c. \(3050\)