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sweet-ann [11.9K]

3 years ago

10

A store has a sale with 10% off every item. When you enter the store, you receive a coupon that states that you receive an addit

ional 40% off. Is this equal to a discount? Explain your answer.
The total percent of reduction is _____% , so this __ * is or is not * __equal to a discount.

1 answer:

sweet [91]3 years ago

7 0

Step-by-step explanation:

Step one:

We are told that the store offers off 10% of sales, this means that the store is offsetting the price down by 10% hence a price reduction.

Moreso, <em>a coupon is a voucher entitling the holder to a discount off a particular product</em>. the coupon is 40%, hence this is equal to a discount, that is price reduction by 40%.

Step two:

<em>Say the price of an item is $100, a coupon if 40% will entitle the holder to only pay $60, that is</em>

=40/100*100

=0.4*100

=$40 off

= 100-40

=$60

<u>The total percent of reduction 10+40= 50%</u>

<u>This is equal to a discount on the sales price</u>

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# # #

A faster way, assuming you know the variance of a linear combination of independent random variables, is to compute

$\mathrm{Var}[W_1+W_2+W_3]$

$=\mathrm{Var}[W_1]+\mathrm{Var}[W_2]+\mathrm{Var}[W_3]+2(\mathrm{Cov}[W_1,W_2]+\mathrm{Cov}[W_1,W_3]+\mathrm{Cov}[W_2,W_3])$

and since the $W_i$ are independent, each covariance is 0. Then

$\mathrm{Var}[W_1+W_2+W_3]=\mathrm{Var}[W_1]+\mathrm{Var}[W_2]+\mathrm{Var}[W_3]$

$\mathrm{Var}[W_1+W_2+W_3]=\dfrac{25}3+\dfrac{100}3+75=\dfrac{350}3$

and take the square root to get the standard deviation.

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