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kodGreya [7K]
3 years ago
10

A store pays a 6% commission on the first $500 in sales and and 8% on sales over $500. Find the commission on an $800 sale

Mathematics
1 answer:
AveGali [126]3 years ago
5 0
First you need to understand the structure of the commission. 
The first part is 6% commission on sales up to $500. 
The second part is 8% commission on sales over $500. 

Note that the second part doesn't mean that a sale of $800 gets 8% of $800. 

It means that once we have reached $500, any *further* sales get 8%. 
Since $800 is $300 more than $500, the commission is 

6% of $500 + 
8% of $300 

The first thing she did was work out the excess above $500. 
Then she worked out the two percentages in two separate parts. 

The second part seems to have incurred a cut and past accident, not sure if that is yours or it was already done.
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An appliance manufacturer claims to have developed a compact microwave oven that consumes a mean of no more than 250 W. From pre
melamori03 [73]

Answer:

We conclude that a compact microwave oven consumes a mean of more than 250 W.

Step-by-step explanation:

We are given that an appliance manufacturer claims to have developed a compact microwave oven that consumes a mean of no more than 250 W with a population standard deviation of 15 W.

They take a sample of 20 microwave ovens and find that they consume a mean of 257.3 W.

Let \mu = <u><em>mean power consumption for microwave ovens.</em></u>

So, Null Hypothesis, H_0 : \mu \leq 250 W     {means that a compact microwave oven consumes a mean of no more than 250 W}

Alternate Hypothesis, H_A : \mu > 250 W     {means that a compact microwave oven consumes a mean of more than 250 W}

The test statistics that would be used here <u>One-sample z test statistics</u> as we know about the population standard deviation;

                                T.S. =  \frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }  ~ N(0,1)

where, \bar X = sample mean power consumption for ovens = 257.3 W

            σ = population standard deviation = 15 W

            n = sample of microwave ovens = 20

So, <em><u>the test statistics</u></em>  =  \frac{257.3-250}{\frac{15}{\sqrt{20} } }

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The value of z test statistics is 2.176.

<u>Now, at 0.05 significance level the z table gives critical value of 1.645 for right-tailed test.</u>

Since our test statistic is more than the critical value of t as 2.176 > 1.645, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which <u>we reject our null hypothesis</u>.

Therefore, we conclude that a compact microwave oven consumes a mean of more than 250 W.

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4.099 is 10 times more than 40.99 : (10 * 40.99) = 409.9 (false)

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