Simplify<br> -3/4(5p-12)+2(8-1/4p)

A carload of steel rods has arrived at Cybermatic Construction Company. The car contains 50,000 rods. Claude Ong, manager of Qua

amid [387]

Answer:

There is a 99.24% probability that Claude's sample has a mean between 119.985 and 120.0125 inches.

Step-by-step explanation:

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 $\frac{\sigma}{\sqrt{n}}$ .

Problems of normally distributed samples can be 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.

In this problem, we have that:

The population of rods has a mean length of 120 inches and a standard deviation of 0.05 inch. This means that $\mu = 120, \sigma = 0.05$ .

Claude Ong, manager of Quality Assurance, directs his crew measure the lengths of 100 randomly selected rods. This means that $n = 100, s = \frac{\sigma}{\sqrt{n}} = \frac{0.05}{\sqrt{100}} = 0.005$ .

The probability that Claude's sample has a mean between 119.985 and 120.0125 inches is

We are working with the sample mean, so we use the standard deviation of the sample, that is, $s$ instead of $\sigma$ in the z score formula.

This probability is the pvalue of Z when $X = 120.0125$ subtracted by the pvalue of Z when $X = 119.985$ .

X = 120.0125

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

$Z = \frac{120.0125 - 120}{0.005}$

$Z = 2.5$

$Z = 2.5$ has a pvalue of 0.9938.

X = 119.985

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

$Z = \frac{119.985 - 120}{0.005}$

$Z = -3$

$Z = -3$ has a pvalue of 0.0014.

So there is a 0.9938 - 0.0014 = 0.9924 = 99.24% probability that Claude's sample has a mean between 119.985 and 120.0125 inches.

7 0

2 years ago

Which expression is modeled by this arrangement of tiles?

Gnoma [55]

Answer:

The answer is 16 ÷ 2 = 8.

Step-by-step explanation:

Now, to find the expression modeled by arrangement of tiles.

So, according to the model in the question.

There are 16 tiles in the model.

So, arrangement of 16 tiles divided into 2 groups.

Where each group consist 8 tiles.

So, we can write as:

$16\div 2$

As 16 is the number of tiles and 2 is the number of groups.

Now, we can check the expression by doing the division.

$16\div 2 = 8$

Therefore, each group has 8 tiles.

6 0

2 years ago

Read 2 more answers

Each of the letters below represents a different digit. if EAT = 721 what does TURKEY represent

zaharov [31]

Thanksgiving

Oh no! Something went wrong while adding your answer
It's too short.<span> Write at least 20 characters to explain it well.</span>

6 0

2 years ago

Based on the graph shown to the right, whose phones cost varies directly with the amount of time spent talking?

Lena [83]

Answer:

B

Step-by-step explanation:

Given 2 quantities that vary directly, then the graph must pass through the origin.

Nikiya's graph is the only one to do this ⇒ B

8 0

2 years ago

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Pooja's plant began sprouting 2days before Pooja bought it, and she had it for 98 days until it died. At its tallest, the plant

taurus [48]

Given that function H(t) models the height of Pooja's plant (in centimeters) where t is the number of days after she bought it.

Now we have to find about which number type is more appropriate for the domain of h. That means what values can be taken by the variable "t".

Since t is number of days not the hours so t will not use decimal or fraction values. It can use integer values for the number of days.

Since time is counted after she bought the plant then number of days will be positive.

Hence answer for the type of domain can be positive integers or you can say integers greater than or equal to 0.

4 0

2 years ago

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Simplify -3/4(5p-12)+2(8-1/4p)