What three different equations that have x = 5 as a solution

A random sample of 36 observations has been drawn from a normal distribution with mean 50 and standard deviation 12. Find the pr

Gre4nikov [31]

Answer:

$z= \frac{47 -50}{\frac{12}{\sqrt{36}}}=-1.5$

$z= \frac{53 -50}{\frac{12}{\sqrt{36}}}=1.5$

And using a calculator, excel ir the normal standard table we have that:

$P(47 \leq \bar X \leq 53) =P(-1.5 \leq Z \leq 1.5)$

And we can calculate the probability like this: $P(-1.5 \leq Z \leq 1.5) = P(z$ Step-by-step explanation:

A random sample of 36 observations has been drawn from a normal distribution with mean 50 and standard deviation 12. Find the probability that the sample mean is in the interval 47<=X<53. Is the assumption of normality important. Why?

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 variable of interest of a population, and for this case we know the distribution for X is given by:

$X \sim N(50,12)$

Where $\mu=50$ and $\sigma=12$

Since the distribution for X is normal then we know that the distribution for the sample mean $\bar X$ is given by:

$\bar X \sim N(\mu, \frac{\sigma}{\sqrt{n}})$

We can find the probability required like this:

$z= \frac{47 -50}{\frac{12}{\sqrt{36}}}=-1.5$

$z= \frac{53 -50}{\frac{12}{\sqrt{36}}}=1.5$

And using a calculator, excel ir the normal standard table we have that:

$P(47 \leq \bar X \leq 53) =P(-1.5 \leq Z \leq 1.5)$

And we can calculate the probability like this:

$P(-1.5 \leq Z \leq 1.5) = P(z$

4 0

1 year ago

The perimeter of a square is represented by the expression 32x - 12.8. Draw a square to represent this situation and label its s

Hoochie [10]

Answer:

Step-by-step explanation:

Given that: The perimeter of a square is: 32x - 12.8

As we all know that, the formula to find the perimeter of a square is:

Sum of the 4 side = 4* length of the side

=> the length of 1 side: The perimeter of a square / 4

In this situation, we have length of 1 side side is:

(32x - 12.8) / 4

= 32/4x - 12.8/4

= 8x - 3.2

The 1st equivalent expressions for the perimeter: 4 *(8x - 3.2)

The 2nd equivalent expressions for the perimeter: (8x - 3.2) + (8x - 3.2) + (8x - 3.2) + (8x - 3.2)

The 3rd equivalent expressions for the perimeter: 2*(8x - 3.2) + 2*(8x - 3.2)

3 0

1 year ago

State the complement of each of the following sets: (a) Engineers with less than 36 months of full-time employment. (b) Samples

iren2701 [21]

Answer:

(a) Engineers with greater than 36 months of full-time employment.

(b) Samples of cement blocks with compressive strength greater than 6000 kilograms per square centimeter

(c) Measurements of the diameter of forged pistons that conform to engineering specifications.

(d) Cholesterol levels that measure less than 180 and greater than 220.

Step-by-step explanation:

The complement of a set refers to elements that does not exist in that set. It means what does not exist in the set but exist in the universal set.

(a) Engineers with greater than 36 months of full-time employment.

In this case, the Universal set is a set of engineers in full-time employment. The given set is for engineers with less than 36 months of full-time employment. The complement is engineers with greater than 36 months of full-time employment.

(b) Samples of cement blocks with compressive strength greater than 6000 kilograms per square centimeter

In this case, the universal set is a set of samples of cement block having compressive strength. The given set is a set of cement block having compressive strength less than 6000 kilograms per square centimeter. The complement is samples of cement blocks with compressive strength greater than 6000 kilograms per square centimeter.

(c) Measurements of the diameter of forged pistons that conform to engineering specifications.

In this case, the universal set is a set of measurements of the diameter of forged pistons. The given set is a set of measurements of the diameter of forged pistons that do not conform to engineering specifications. The complement is a set of measurements of the diameter of forged pistons that conforms to engineering specification.

(d) Cholesterol levels that measure less than 180 and greater than 220.

In this case, the universal set is a set of Cholesterol levels. The given set is Cholesterol levels that measure greater than 180 and less than 220. The complement is Cholesterol levels that measure less than 180 and greater than 220.

5 0

1 year ago

Using the standard normal table, the probability that Seth’s light bulb will last no more than 14,500 (P(z ≤ 1.25)) hours is abo

lana66690 [7]

Answer:

How many standard deviations above the mean is 14,500 hours? 1.25 1.5 2.5 Using the standard normal table, the probability that Seth's light bulb will last no more than 14,500 (P(z ≤ 1.25)) hours is about ✔ 89% .

5 0

1 year ago

Read 2 more answers

this net will be folded to form a prism. which pairs of faces will be opposite one another when the prism is created? check all

lesya [120]

Answer:

d and f 2.a and c 3.b and e

Step-by-step explanation:

6 0

1 year ago