<img src="https://tex.z-dn.net/?f=65%20%5Ctimes%2098%20%5Cdiv%2032%20-%2065%20%5Ctimes%207544" id="TexFormula1" title="65 \times

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ss7ja [257]

3 years ago

98 \div 32 - 65 \times 7544" alt="65 \times 98 \div 32 - 65 \times 7544" align="absmiddle" class="latex-formula">

Mathematics

1 answer:

Volgvan3 years ago

4 0

65 * 98 / 32 - 65 * 7544 =
6370 / 32 - 490360 =
199.0625 - 490360 =
-490160.9375

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The amount of coffee that a filling machine puts into an 8-ounce jar is normally distributed with a mean of 8.2 ounces and a sta

nordsb [41]

Answer:

73.30% probability that the sampling error made in estimating the mean amount of coffee for all 8-ounce jars by the mean of a random sample of 100 jars will be at most 0.02 ounce

Step-by-step explanation:

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

Normal probability distribution

Problems of normally distributed samples are solved using 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.

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 problem, we have that:

$\mu = 8.2, \sigma = 0.18, n = 100, s = \frac{0.18}{\sqrt{100}} = 0.018$

What is the probability that the sampling error made in estimating the mean amount of coffee for all 8-ounce jars by the mean of a random sample of 100 jars will be at most 0.02 ounce?

This is the pvalue of Z when X = 8.2 + 0.02 = 8.22 subtracted by the pvalue of Z when X = 8.2 - 0.02 = 8.18. So

X = 8.22

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

By the Central Limit Theorem

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

$Z = \frac{8.22 - 8.2}{0.018}$

$Z = 1.11$

$Z = 1.11$ has a pvalue of 0.8665

X = 8.18

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

$Z = \frac{8.18 - 8.2}{0.018}$

$Z = -1.11$

$Z = -1.11$ has a pvalue of 0.1335

0.8665 - 0.1335 = 0.7330

73.30% probability that the sampling error made in estimating the mean amount of coffee for all 8-ounce jars by the mean of a random sample of 100 jars will be at most 0.02 ounce

8 0

4 years ago

What is 85.23 - 2.675 =?

Anna007 [38]

Your answer is 85.555,hope this helped or 85.5 with - over it

8 0

3 years ago

Read 2 more answers

Christopher scored 7 more than two times the questions Mathew scored on the math test. If Christopher scored 87 on the math test

viktelen [127]

Answer:

Step-by-step explanation:

To solve this, we can create an equation that represents this situation. Since Christopher score 7 more than twice what Mathew scored, the equation will be:

C = 2M + 7

(Variables are representative of the first letter of each name)

Seeing as Christopher scored 87, we can put that into the equation and solve for M.

So, the equation will be:

87 = 2M + 7

Subtract 7 from both sides in order to isolate variable M on the right side.

80 = 2M

Now solve for M, which is 40 (divide both sides by 2).

7 0

3 years ago

8 points

Zigmanuir [339]

Answer:

10/40 = 25%

Step-by-step explanation:

40 total = denominator

30 cheese - 40 total = 10 not cheese

10/40

8 0

3 years ago

Find the indicator real nth root

ankoles [38]

It can be useful to know the prime factorization of the number:

$256 = 2^8$

Then, remember that the n-th root of a number is the same as that number to the 1/n-th power:

$\sqrt[4]{256} = 256^{\frac{1}{4}}$

Finally, you have to remember the rule for raising a power to another power, i.e. you multiply the exponents:

$(a^b)^c = a^{bc}$

Put together everything we said so far to write

$\sqrt[4]{256} = 256^{\frac{1}{4}} = (2^8)^{\frac{1}{4}} = 2^{\frac{8}{4}} = 2^2 = 4$

3 0

3 years ago