Mathematics, 20.01.2020 20:31 stef76

The mean weight of loads of rock is 42.0 tons with a standard deviation of 12.0 tons. if 25 loads are chosen at random for a weight check, find the probability that the mean weight of those loads is less than 40.7 tons. assume that the variable is normally distributed.

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Answer from: garrismunoz

$P(\bar X$

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".

Solution to the problem

Let X the random variable that represent the weigths of rock from population, and for this case we know the distribution for X is given by:

$X \sim N(42,12)$

Where $\mu=42$ and $\sigma=12$

The distribution for the sample mean $\bar X$ is given by:

$\bar X \sim N(\mu= 42, \sigma_{\bar X}=\frac{\sigma}{\sqrt{n}}=\frac{12}{\sqrt{25}}=2.4)$

For this case we want to find this probability:

$P(\bar X$

And for this we can use the z score given by:

$z = \frac{\bar x -\mu}{\sigma_{\bar X}}$

And if we use this formula we got:

$P(\bar X$

And if we use the normal standard table or excel we find the probability:

$P(\bar X$

Answer from: Quest

step-by-step explanation:

hello and welcome!

so, when we see the words "proportional" along with a table, we need to know that we're looking numbers that divide by the same thing.

looking at this table, we simply have to do a trial and error, and divide to see which numbers have the same quotient. if you look at choice a & c, they both have equal quotients for three of the numbers, with one exception, so those can't be the answer. looking at b, there is no similarity, so that can't be it. then, we see d; if you divide all the numbers in the table, you'll see that they all divide by two, which is a proportional relationship, and our answer!

$4/2 = 2\\7/3.5=2\\8/4=2\\10/5=2$

also, always remember that the x will always be the number that goes into y, and somewhere behind this table, is a formula. for this specific table, the formula would be:

$y=\frac{x}{2}$

since our x-value is being divided by two to get the y-value. and if they were to ask for more numbers in the series, this is the formula you would use to find them.

Answer from: Quest

the answer is 48m^2!

step-by-step explanation:

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