Which statement is true regarding the graphed functions? Can someone help me out?

According to records, the amount of precipitation in a certain city on a November day has a mean of inches, with a standard devi

Mekhanik [1.2K]

Answer:

The probability that the mean daily precipitation will be of X inches or less for a random sample of n November days is the p-value of $Z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}$ , in which $\mu$ is mean amount of inches of rain and $\sigma$ is the standard deviation.

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 normal distributions can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the z-score 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 p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem establishes 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 question:

Mean $\mu$ , standard deviation $\sigma$

n days:

This means that $s = \frac{\sigma}{\sqrt{n}}$

Applying the Central Limit Theorem to the z-score formula.

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

What is the probability that the mean daily precipitation will be of X inches or less for a random sample of November days?

The probability that the mean daily precipitation will be of X inches or less for a random sample of n November days is the p-value of $Z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}$ , in which $\mu$ is mean amount of inches of rain and $\sigma$ is the standard deviation.

5 0

3 years ago

Find the sum of the series. ∞ 5(−1)nπ2n + 1 32n + 1(2n + 1)! n = 0

wlad13 [49]

Could you give the question more clear?

5 0

4 years ago

Beth started a workout program. On Monday, she did 15 sit-ups.

Studentka2010 [4]

On Friday, Beth will most likely do 39 sit ups. Every day she is doing an extra 6 sit ups.... Thursday would be 33 sit ups and Friday would be 39 sit ups.

3 0

4 years ago

What does p equal when p=210e^(0.0069*20)?

Korolek [52]

p=210e^(0.0069*20)
'e' is a mathematical constant equal to 2.718281828459

0.0069*20 = .138

e^.138 =

2.718281828459^.138 =

 1.1479755503 
210 * 1.1479755503 =

 241.074865563

5 0

3 years ago

Maurice and Johanna have appreciated the help you have provided them and their company Pythgo-grass. They have decided to let yo

jasenka [17]

1.A triangular section of a lawn will be converted to river rock instead of grass. Maurice insists that the only way to find a missing side length is to use the Law of Cosines. Johanna exclaims that only the Law of Sines will be useful. Describe a scenario where Maurice is correct, a scenario where Johanna is correct, and a scenario where both laws are able to be used. Use complete sentences and example measurements when necessary.

The Law of Cosines is always preferable when there's a choice. There will be two triangle angles (between 0 and 180 degrees) that share the same sine (supplementary angles) but the value of the cosine uniquely determines a triangle angle.

To find a missing side, we use the Law of Cosines when we know two sides and their included angle. We use the Law of Sines when we know another side and all the triangle angles. (We only need to know two of three to know all three, because they add to 180. There are only two degrees of freedom, to answer a different question I just did.

2.An archway will be constructed over a walkway. A piece of wood will need to be curved to match a parabola. Explain to Maurice how to find the equation of the parabola given the focal point and the directrix.

We'll use the standard parabola, oriented in the usual way. In that case the directrix is a line y=k and the focus is a point (p,q).

The points (x,y) on the parabola are equidistant from the line to the point. Since the distances are equal so are the squared distances.

The squared distance from (x,y) to the line y=k is $(y-k)^2$

The squared distance from (x,y) to (p,q) is $(x-p)^2+(y-q)^2.$ 
These are equal in a parabola:


$(y-k)^2 =(x-p)^2+(y-q)^2$ 

 $y^2-2ky + k^2 =(x-p)^2+y^2-2qy + q^2$

$y^2-2ky + k^2 =(x-p)^2 + y^2 - 2qy+ q^2$

$2(q-k)y =(x-p)^2+ q^2-k^2$

$y = \dfrac{1}{2(q-k)} ( (x-p)^2+ q^2-k^2)$

Gotta go; more later if I can.

3.There are two fruit trees located at (3,0) and (−3, 0) in the backyard plan. Maurice wants to use these two fruit trees as the focal points for an elliptical flowerbed. Johanna wants to use these two fruit trees as the focal points for some hyperbolic flowerbeds. Create the location of two vertices on the y-axis. Show your work creating the equations for both the horizontal ellipse and the horizontal hyperbola. Include the graph of both equations and the focal points on the same coordinate plane.

4.A pipe needs to run from a water main, tangent to a circular fish pond. On a coordinate plane, construct the circular fishpond, the point to represent the location of the water main connection, and all other pieces needed to construct the tangent pipe. Submit your graph. You may do this by hand, using a compass and straight edge, or by using a graphing software program.

5.Two pillars have been delivered for the support of a shade structure in the backyard. They are both ten feet tall and the cross-sections of each pillar have the same area. Explain how you know these pillars have the same volume without knowing whether the pillars are the same shape.

3 0

3 years ago