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Dvinal [7]
2 years ago
12

Your little brother wants hot chocolate ot be 150 degrees, but you accidentally heated the water to 175 degrees. If after 5 minu

tes the temperature is 165 and the temperature in your house is 70 degrees, how long will your little brother have to wait to drink his hot chocolate?
Mathematics
2 answers:
attashe74 [19]2 years ago
7 0
<h3><u>Answer:</u></h3>
  • My little brother will have to wait for 12.5 minutes to drink his hot chocolate.
<h3><u>Step-by-step explanation:</u></h3>

We know that in 5 minutes, the temperature of the hot chocolate decreased by 10 degrees. We also know that the temperature is fixed at 70 degrees. Now, using the info given, let's solve!

  • => 5 minutes = 10 degrees decrease
  • => 1 minute = 2 degrees decrease
  • => 1 minute x 12.5 = 2 x 12.5 degrees decrease
  • => 12.5 minutes = 25 degrees decrease
<h3><u>Conclusion:</u></h3>

Therefore, my little brother will have to wait for 12.5 minutes to drink his hot chocolate.

Hoped this helped.

BrainiacUser1357

Ber [7]2 years ago
3 0

Answer:

12.5 minutes

Step-by-step explanation:

it takes 5 minutes to cool 10 degrees

after ten minutes it would be 20 degrees less

then after 2.5 minutes it would be 5 degrees less

so it would take you 12.5 minutes to get 25 degrees less

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Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

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:

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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.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean \mu and standard deviation \sigma, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \mu and standard deviation s = \frac{\sigma}{\sqrt{n}}.

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

In this question, we have that:

\mu = 200, \sigma = 50, n = 100, s = \frac{50}{\sqrt{100}} = 5

a. What is the probability that the sample mean will be within +/- 5 of the population mean (to 4 decimals)?

This is the pvalue of Z when X = 200 + 5 = 205 subtracted by the pvalue of Z when X = 200 - 5 = 195.

Due to the Central Limit Theorem, Z is:

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

X = 205

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

Z = \frac{205 - 200}{5}

Z = 1

Z = 1 has a pvalue of 0.8413.

X = 195

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

Z = \frac{195 - 200}{5}

Z = -1

Z = -1 has a pvalue of 0.1587.

0.8413 - 0.1587 = 0.6426

0.6426 = 64.26% probability that the sample mean will be within +/- 5 of the population mean.

b. What is the probability that the sample mean will be within +/- 10 of the population mean (to 4 decimals)?

This is the pvalue of Z when X = 210 subtracted by the pvalue of Z when X = 190.

X = 210

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

Z = \frac{210 - 200}{5}

Z = 2

Z = 2 has a pvalue of 0.9772.

X = 195

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

Z = \frac{190 - 200}{5}

Z = -2

Z = -2 has a pvalue of 0.0228.

0.9772 - 0.0228 = 0.9544

0.9544 = 95.44% probability that the sample mean will be within +/- 10 of the population mean.

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