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3 years ago

Felicia makes \frac{1}{2}

Mathematics

1 answer:

saw5 [17]3 years ago

3 0

Question:

Felicia makes ½ gallon of fruit punch. She pours an equal amount into 8 glasses.

What fraction of a gallon fruit punch is in each glass?

Answer:

The fraction of a gallon fruit punch is in each glass is 1/16

Step-by-step explanation:

Given

Size of fruit punch = ½ gallon

Number of glass = 8

Required

Fraction of a gallon fruit punch is in each glass?

To solve this question, the following assumption has to be made.

- The 8 glass cups are of equal sizes.

Having said that;

The interpretation of the question is that, the fruit is evenly distributed into the 8 glass cups.

Mathematically, the size of the fruit punch will be divided by the number of glass cups.

So, we have

Fraction = ½ ÷ 8 (convert ÷ to *)

Fraction = ½ * ⅛

Fraction = 1/16

Hence, the fraction of a gallon fruit punch is in each glass is 1/16

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3 years ago

The realtor and her clients do not know the average home sale price for all of Guelph (500 was actually just a guess). However,

strojnjashka [21]

Answer:

a) The 99% confidence interval would be given by (346.708;453.292)

b) The 99% confidence interval would be given by (338.445;461.555)

Step-by-step explanation:

1) Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

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

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$\bar X=400$ represent the sample mean for the sample

$\mu$ population mean (variable of interest)

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n=15 represent the sample size

2) Part a

The confidence interval for the mean is given by the following formula:

$\bar X \pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}$ (1)

Since the Confidence is 0.99 or 99%, the value of $\alpha=0.01$ and $\alpha/2 =0.005$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-NORM.INV(0.005,0,1)".And we see that $z_{\alpha/2}=2.58$

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

$400-2.58\frac{80}{\sqrt{15}}=346.708$

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So on this case the 99% confidence interval would be given by (346.708;453.292)

3) Part b

For this case we don't know the population deviation so we need to use the t distribution instead the normal standard distribution.

The confidence interval for the mean is given by the following formula:

$\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}$ (1)

We need to find the degrees of freedom first df=n-1=15-1=14

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

$400-2.98\frac{80}{\sqrt{15}}=338.445$

$400+2.98\frac{80}{\sqrt{15}}=461.555$

So on this case the 99% confidence interval would be given by (338.445;461.555)

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3 years ago

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