Mathematics, 19.02.2020 04:00 kylabreanne120

A vending machine automatically pours soft drinks into cups. The amount of soft drink dispensed into a cup is normally distributed with a mean of 7.6 ounces and standard deviation of 0.4 ounce. Examine the figure below and answer the following questions.
(a) Estimate the probability that the machine will overflow an 8-ounce cup. (Round your answer to two decimal places.)
1
(b) Estimate the probability that the machine will not overflow an 8-ounce cup. (Round your answer to two decimal places.)
2
(c) The machine has just been loaded with 868 cups. How many of these do you expect will overflow when served?
3 cups

Answers: 2

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Answer from: dpranavesh446

a) $P(X8)=P(\frac{X-\mu}{\sigma}\frac{8-\mu}{\sigma})=P(Z\frac{8-7.6}{0.4})=P(Z1)$

And we can find this probability using the complement rule and the standard normal table or excel:

P(Z1)=1-P(Z

b) P(X

And we can find this probability using the standard normal table or excel:

P(Z

c) For this case we have a total of 868 cups and we know that the fraction of cups that will be overflow is 0.159, so then the expected number of cups overflow would be:

$N = 868*0.159= 138.012 \approx 138$

Step-by-step explanation:

Previous concepts

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 Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".

Part a

Let X the random variable that represent the amount of soft frink of a population, and for this case we know the distribution for X is given by:

$X \sim N(7.6,0.4)$

Where $\mu=7.6$ and $\sigma=0.4$

We are interested on this probability

P(X8)

And the best way to solve this problem is using the normal standard distribution and the z score given by:

$z=\frac{x-\mu}{\sigma}$

If we apply this formula to our probability we got this:

$P(X8)=P(\frac{X-\mu}{\sigma}\frac{8-\mu}{\sigma})=P(Z\frac{8-7.6}{0.4})=P(Z1)$

And we can find this probability using the complement rule and the standard normal table or excel:

P(Z1)=1-P(Z

Part b

We are interested on this probability

P(X

And the best way to solve this problem is using the normal standard distribution and the z score given by:

$z=\frac{x-\mu}{\sigma}$

If we apply this formula to our probability we got this:

P(X

And we can find this probability using the standard normal table or excel:

P(Z

Part c

For this case we have a total of 868 cups and we know that the fraction of cups that will be overflow is 0.159, so then the expected number of cups overflow would be:

$N = 868*0.159= 138.012 \approx 138$

Answer from: Quest

oof cheaters cheat because they’re lazy that’s why i cheat xd

: )

step-by-step explanation:

Answer from: Quest

total amount of money that he should pay if he has not used his duty free exemption is $98

step-by-step explanation:

given a united states citizen returning to the states declares the following items at the customs office: 3 shirts at $8.50 each 2 dresses at $27.50 each 1 pair of gold cuff links at $17.50 per pair. we have to find how much he pay

cost of 3 shirts if one cost at $8.50 is $3\times 8.50=$25.5$

cost of 2 dresses if one cost at $27.50 is $2\times 27.50=$55$

cost of 1 pair of gold cuff at $17.50

so, total amount of money that he should pay if he has not used his duty free exemption is $25.5+$55+$17.50=$98

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