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3 years ago

14

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(1 - 6x)" alt="24x - 22 = - 4(1 - 6x)" align="absmiddle" class="latex-formula">
what is x

2 answers:

Step2247 [10]3 years ago

6 0

Answer:

x = 18

Step-by-step explanation:

distribute 4

24x - 22 = -4 + 24x

put the x's on one side.

x = -4 +22

x = 18

Nikitich [7]3 years ago

5 0

Answer:

No solution

Step-by-step explanation:

24x - 22 = -4 ( 1 - 6x )

24x - 22 = -4 + 24x

24x - 18 = 24x

No solution

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stepan [7]

Answer:

27.43% probability that the mean volume of a random sample of 144 bottles is less than 12 oz.

Step-by-step explanation:

To solve this problem, it is important 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 random variable X, with mean $\mu$ and standard deviation $\sigma$ , a large sample size can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$

In this problem, we have that:

$\mu = 12.01, \sigma = 0.2, n = 144, s = \frac{0.2}{\sqrt{144}} = 0.0167$

What is the probability that the mean volume of a random sample of 144 bottles is less than 12 oz

This is the pvalue of Z when $X = 12$

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

By the Central Limit Theorem

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

$Z = \frac{12 - 12.01}{0.0167}$

$Z = -0.6$

$Z = -0.6$ has a pvalue of 0.2743.

So there is a 27.43% probability that the mean volume of a random sample of 144 bottles is less than 12 oz.

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