22.05.2022

A soft drink-dispensing machine uses paper cups that hold a maximum of 12 ounces. The machine is set to dispense a mean of 10 ounces of the drink. Because of an imprecise process, the amount dispensed actually varies; it is normally distributed with a standard deviation of 1 ounce. If we simulated the filling process, and had the random number .564, how many ounces would the cup contain? Give your answer to 3 decimal places.

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Step-by-step answer

24.06.2023, solved by verified expert
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The cup would contain 10.16 ounces.

Step-by-step explanation:

When the distribution is normal, we use the z-score formula.

In a set with mean A soft drink-dispensing machine uses paper cups, №17886488, 22.05.2022 23:34 and standard deviation A soft drink-dispensing machine uses paper cups, №17886488, 22.05.2022 23:34, the zscore of a measure X is given by:

A soft drink-dispensing machine uses paper cups, №17886488, 22.05.2022 23:34

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Mean of 10 ounces, standard deviation of 1 ounce:

This means that A soft drink-dispensing machine uses paper cups, №17886488, 22.05.2022 23:34

If we simulated the filling process, and had the random number .564, how many ounces would the cup contain?

This means that we have to find X when Z has a pvalue of 0.564. So X when Z = 0.16. So

A soft drink-dispensing machine uses paper cups, №17886488, 22.05.2022 23:34

A soft drink-dispensing machine uses paper cups, №17886488, 22.05.2022 23:34

A soft drink-dispensing machine uses paper cups, №17886488, 22.05.2022 23:34

A soft drink-dispensing machine uses paper cups, №17886488, 22.05.2022 23:34

The cup would contain 10.16 ounces.

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Mathematics
Step-by-step answer
P Answered by PhD

The cup would contain 10.16 ounces.

Step-by-step explanation:

When the distribution is normal, we use the z-score formula.

In a set with mean \mu and standard deviation \sigma, the zscore of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Mean of 10 ounces, standard deviation of 1 ounce:

This means that \mu = 10, \sigma = 1

If we simulated the filling process, and had the random number .564, how many ounces would the cup contain?

This means that we have to find X when Z has a pvalue of 0.564. So X when Z = 0.16. So

Z = \frac{X - \mu}{\sigma}

0.16 = \frac{X - 10}{1}

X - 10 = 0.16*1

X = 10.16

The cup would contain 10.16 ounces.

Mathematics
Step-by-step answer
P Answered by PhD
Answer: 440 grams for 1.54 is the better value
Explanation:
Take the price and divide by the number of grams
1.54 / 440 =0.0035 per gram
1.26 / 340 =0.003705882 per gram
0.0035 per gram < 0.003705882 per gram
Mathematics
Step-by-step answer
P Answered by PhD

The solution is given in the image below

The solution is given in the image below
Mathematics
Step-by-step answer
P Answered by PhD

The wood before starting =12 feet

Left wood=6 feet

Wood used till now=12-6=6 feet

Picture frame built till now= 6/(3/4)

=8 pieces

Therefore, till now 8 pieces have been made.

Mathematics
Step-by-step answer
P Answered by PhD

Cost before sale tax=$46.00

Cost after including tax=$48.76

Sale tax=$48.76-46.00

=$2.76

we know,

sale tax=((sales tax rate)/100) * cost before sale tax

2.76=((sales tax rate)/100) *46.00

sale tax rate=(2.76*100)/46

                   =276/46

                    =6%

There fore sales tax rate=6%

Mathematics
Step-by-step answer
P Answered by PhD

Cost of 6 gallons =$15

Cost of 1 gallon =15/6

                           =$2.5

Cost of 7 gallons=$2.5 * 7

                           =$17.5

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