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Mathematics
ikr2002:

If Ziggy’s Taco Shop delivers dinners with a mean time of 21 minutes and a standard deviation of 4 minutes and Sheila’s Burrito Emporium delivers dinners with a mean time of 19 minutes and a standard deviation of 6 minutes, which place would be better to order from to receive your dinner at most 15 minutes from the time you place it? Show all relevant work and explain what your answer means.

AZ:

So I just drew it out roughly although I don't really think it's going to help |dw:1623968295352:dw| But to answer this question, you need to understand the concept of standard deviation. Ziggy's taco shop will deliver dinner with a mean of 21 minutes. That means 50% of the time, it'll be over 21 minutes, the other 50% it's delivered in under 21 minutes. With standard deviation, we know that one standard deviation above and below contains 68% of the values So 21 + 4 = 25 21 - 4 = 17 so 68% of the time, your dinner from Ziggy's will be delivered within 17 to 25 minutes Does that make sense so far?

ikr2002:

yeah that's what I was thinking but I would be struggling with which one is better.

AZ:

Here's a more detailed standard deviation curve

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ikr2002:

ah I see

AZ:

Your question wants to know which store is better in receiving dinner within 15 minutes max Ziggy has a mean of 21 with a SD (standard deviation) of 4 21 - 4 = 17 17 - 4 = 13 so if we go 2 SD below the mean, that's all the possible values that the dinner gets delivered in under 15 minutes similarly, can you figure out how much it is for Sheila's restaurant? The mean is 19 and the SD is 6

ikr2002:

19 - 6 = 13 13 - 6 = 7 Would those be it?

AZ:

So like for Ziggy's if we were to make a graph for it what we're looking to find is how much of the time do they deliver in under 15 minutes and that would be what I colored in orange We're essentially comparing the restaurants and trying to find out which place delivers food faster

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AZ:

@ikr2002 wrote:
19 - 6 = 13 13 - 6 = 7 Would those be it?
You only had to subtract 6 once and you get 13 That's going to be only one standard deviation away from the mean of 19 does that make sense?

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AZ:

Because we're trying to find the time it takes for it to be delivered under 15 minutes 13 is the closest number but in the graph I just shaded a little more to (approximately) include until 15 does that make sense

ikr2002:

So why did you subtract the SD twice for Ziggy's but only once for Sheila's?

ikr2002:

Is it just trying to get under 15?

AZ:

because look at the first graph for ziggy everything on the left side of 21 would be 50% of the time we want to find the number where 15 would appear is 15 one standard deviation away or two? 21 - 4 = 17 it's not one standard deviation away 17 - 4 = 13 so it's somewhere in between 1 and 2 standard deviations but for the other one, when you subtract the number once. You get 15 so it's less than one standard deviation but not one standard deviation exactly

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ikr2002:

So then Sheila's be the best option since it's only one SD away instead of two like Ziggy's?

AZ:

yes, because they deliver food more quickly in under 15 minutes

AZ:

if you want an approximate number, you can add those percentages in the shaded area but you can also see from the graph that Sheila delivers more faster than Ziggy's

ikr2002:

Awesome thank you! Now I've got one more question:/

AZ:

No problem! Hopefully that makes sense :)

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