Chapter 10.5, Problem 21PPS

To determine

To calculate the new average price for SUVs and luxury cars.

Answer to Problem 21PPS

The new average price for SUVs and luxury cars is $37,750.

Explanation of Solution

Given information:

15 SUVs priced between $33,000 and $37,000.

5 luxury cars priced between $44,000 and $48,000.

Average price for all of the vehicles= $39,250.

Formula used:

Mean formula is,

  $\overline{X}=\frac{{\displaystyle \sum fX}}{N}$

Where, f is frequency

N is total number of items

X is item.

Calculation:

For mean,

Substituting the values in the mean formula,

  $AveragepriceforSUVsandluxurycars=\frac{priceof15SUVs+priceof5luxurycars}{totalcars}$

Substituting the values,

  $39,250=\frac{priceof15SUVs+priceof5luxurycars}{20}$

Cross multiply both the sides,

  $39,250\times 20=priceof15SUVs+priceof5luxurycars$

On solving,

  $priceof15SUVs+priceof5luxurycars=785,000$

Accoding to question

Prices of all 15 SUVs reduced by 2000 per vehical.

For,the new average price for SUVs and luxury cars

  $=\frac{(priceof15SUVs+priceof5luxurycars)-pricereducedperSUV\times 15}{totalcars}$

Substituting values,

= $\frac{(priceof15SUVs+priceof5luxurycars)-2000\times 15}{totalcars}$

On solving,

  $=\frac{785000-30000}{20}$

On solving,

  $=37,750$

Hence, the new average price for SUVs and luxury ars is $37,750.