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3 years ago

5

Aldos coffee shop makes a blend that is a mixture of two types of coffee. Type A coffee costs Aldo $5.80 per pound, and type of

B coffee costs $4.65 per pound. This month, Aldo made 156 pounds of the blend, for a total cost of $826.60. How many pounds of type B coffee did he use?

1 answer:

LuckyWell [14K]3 years ago

5 0

Let A represent amount of Type A coffee pounds used.
Let B represent amount of Type B coffee pounds used

A + B = 156
B = 156 - A
A = 156 - B

5.80A + 4.65B = 826.60
580 (156 - B) + 4.65B - 826.60 = 0
904.8 - 5.80B + 4.65B - 826.60 = 0
904.8 - 1.15B - 826.60 = 0
78.2 - 1.15B = 0
78.2/1.15 = 1.15B/1.15
68 = B
B = 68 pounds of Type B coffee

There's many more steps you can take to check and etc but am too lazy to put down sorry.

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Previous concepts and data given

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The central limit theorem states that "if we have a population with mean μ and standard deviation σ and take sufficiently large random samples from the population with replacement, then the distribution of the sample means will be approximately normally distributed. This will hold true regardless of whether the source population is normal or skewed, provided the sample size is sufficiently large".

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$s=4.77$ represent the sample standard deviation

n=19 represent the sample selected

$\alpha$ significance level

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Null hypothesis: $\mu = 100$

Alternative hypothesis: $\mu \neq 100$

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And we can calculate the Standard error for the mean like this:

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Now we have everything in order to replace into formula (1):

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Part b

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Alternative hypothesis: $\mu > 100$

The only thing that changes is the p value and would be given by:

$p_v =P(t_{18}>-1.124)=0.862$

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