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Vanyuwa [196]
2 years ago
9

The Foldgers Black Silk K-cup coffee pods weigh on average .28 ounces with a standard deviation of .05 ounces. Answer each of th

e questions.
68%, 2.5%, 81.5%, 95%, 41-42, 20-21, 16%, 84%, 121-122, 5%, 87-88, 64, 35-36
What percentage of K-cups can be expected to fall within 2 Standard Deviations of the mean?

What is the probability that a K-cup will have more than .33 ounces?

Sam's club sells K-cups in a box of 128. How many of them will weigh less than .23 ounces?

K-cups that are more than 2 SD below the mean are considered to be to "weak". What percentage of K-cup are considered to "weak"

In a standard box of 44 k-cups, how many will weigh between .23 and .38 ounces

The ideal weight for K-cups are within 1 SD of the mean, how many of the Sam's Club box of K-cups are ideal?
Mathematics
1 answer:
iragen [17]2 years ago
7 0

Using the Empirical Rule, it is found that:

  • 95% of K-cups can be expected to fall within 2 Standard Deviations of the mean.
  • 0.16 = 16% probability that a K-cup will have more than .33 ounces.
  • 20 of them will weight <u>less than 0.23 ounces.</u>
  • 2.5% of K-cups are considered weak.
  • 36 will weigh <u>between 0.23 and 0.38 ounces</u>.
  • 30 of the Sam's Club box of K-cups are ideal.

The Empirical Rule states that, for a normally distributed random variable:

Approximately 68% of the measures are <u>within 1 standard deviation</u> of the mean.

Approximately 95% of the measures are <u>within 2 standard deviation</u>s of the mean.

Approximately 99.7% of the measures are <u>within 3 standard deviations</u> of the mean.

In this problem:

  • The mean is of 0.28 ounces.
  • The standard deviation is of 0.05 ounces.

First, by the <u>Empirical Rule</u>, 95% of K-cups can be expected to fall within 2 Standard Deviations of the mean.

0.33 ounces is <u>one standard deviation above the mean</u>.

  • 68% of the measures are between 0.23 and 0.33 ounces.
  • The normal distribution is symmetric, which means that of the remaining 100 - 68 = 32%, 16% are less than 0.23 ounces and 16% are more than 0.33 ounces, thus:

0.16 = 16% probability that a K-cup will have more than .33 ounces.

16% weigh <u>less than 0.23 ounces.</u> Out of 128:

0.16(128) = 20

20 of them will weight <u>less than 0.23 ounces.</u>

5% of the measures are more than 2 SD from the mean. Due to the symmetry of the normal distribution, 2.5% are more than 2 SD below the mean, thus, 2.5% of K-cups are considered weak.

  • 0.23 is one standard deviation below the mean.
  • 0.38 is two standard deviations above the mean.
  • Of the 50% below the mean, 68% are above 0.23.
  • Of the 50% above the mean, 95% are below 0.38.

Thus, the proportion <u>between 0.23 and 0.38</u> is:

p = 0.68(0.50) + 0.95(0.5) = 0.815

Out of 44:

0.815(44) = 36

36 will weigh <u>between 0.23 and 0.38 ounces</u>.

68% are within 1 standard deviation of the mean.

Out of 44:

0.68(44) = 30

30 of the Sam's Club box of K-cups are ideal.

A similar problem is given at brainly.com/question/13503878

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When graphing y = 2x2 + 35x + 75, which viewing window would allow you to see all of the intercepts and the minimum as closely a
djverab [1.8K]

The intercept with the y-axes occurs when x = 0

f(0) = 2*02 + 35*0 + 75 = 0 + 0 + 75 = 75

So intercept with x axes is the point (0,75)

The intercept with the x-axes occurs when y=0

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<span>As there’s no direct way to find x, we can use the <span>Bhaskara formula:</span></span>

x=(-b+- square root (b2-4ac))/(2a)

This formula is for: ax2 +bx + c = 0

So:

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x=(-35+- square root (35^2-4*2*75))/(2*2)

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So intercept with y axes are the points (-2.5,0) and (-15,0)

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Xv = -b/(2*a) = -35/(2*2) = -8.75

Yv = f(Xv) = f(-8.75) = 2(-8.75)^2 + 35(-8.75) <span> + 75 = </span>-78.125

So the minimum is the point (-8.75, -78.125)

You can easily verify all these data with a graphic software such as GeoGebra.

Here is the complete list of all the points we need to see:

(0,75); (-2.5,0) ; (-15,0), (-8.75, -78.125)

So the mínimum X has to be -15 and the máximum X has to be 0

and the mínimum Y has to be -78.125 and the máximum Y has to be 75

So this leads to a different scale for X and for Y.


Window x = [ -15, 0] y = [ -78.125, 75]
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