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Anit [1.1K]
3 years ago
9

A store has clearance items that have been marked down by 50%. They are advertising an additional markdown of 25% off the cleara

nce price. A cashmere sweater has an original price of $345, but is now a clearance item. What will the final price of the sweater be after all discounts are applied? Round your answer to the nearest cent.
Mathematics
1 answer:
luda_lava [24]3 years ago
4 0

The final price of the sweater after all discounts are applied will be $129.38

<em><u>Explanation</u></em>

A cashmere sweater has an original price of $345

So, the clearance price after 50% marked down will be: 345-(345*0.50)=345-172.5 = 172.5 dollar

Now, the additional markdown is 25% of the clearance price. So, the additional marked down amount = 172.5 *0.25 = 43.125 dollar

So, the final price of the sweater after all discounts are applied will be : (172.5-43.125) dollar = 129.375 dollar = $ 129.38  (Rounding to the nearest cent)

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Previous concepts

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Solution to the problem

Let X the random variable that represent the IQ scores of a population, and for this case we know the distribution for X is given by:

X \sim N(100,15)  

Where \mu=100 and \sigma=15

We select a sample of n=16 and we are interested on the distribution of \bar X, since the distribution for X is normal then we can conclude that the distribution for \bar X is also normal and given by:

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Because by definition:

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E(\bar X) = \mu

Var(\bar X) = \frac{\sigma^2}{n}

And for this case we have this:

\mu_{\bar X}= \mu = 100

\sigma_{\bar X} = \frac{15}{\sqrt{16}}= 3.75

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