What number divided by -4 equals -3?

A sample of size 45 will be drawn from a population with mean 53 and standard deviation 11. Use the TI-84 Plus calculator. (a) I

sukhopar [10]

Answer:

a) We have the standard deviation and the mean, so it is appropriate to use the normal distribution to find probabilities for x.

b) There is a 15.97% probability that x will be between 54 and 55.

c) The 47th percentile of x is $X = 52.877$ .

Step-by-step explanation:

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

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

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. Subtracting 1 by the pvalue, we This p-value is the probability that the value of the measure is greater than X.

A sample of size 45 will be drawn from a population with mean 53 and standard deviation 11.

This means that $\mu = 53$ .

We have to find the standard deviation of the sample, that is:

$\sigma = \frac{11}{\sqrt{45}} = 1.64$

(a) Is it appropriate to use the normal distribution to find probabilities for x?

We have the standard deviation and the mean, so it is appropriate to use the normal distribution to find probabilities for x.

(b) Find the probability that x will be between 54 and 55.

This is the pvalue of the Z score when X = 55 subtracted by the pvalue of the Z score when X = 54.

X = 55

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

$Z = \frac{55 - 53}{1.64}$

$Z = 1.22$

$Z = 1.22$ has a pvalue of 0.88877.

X = 54

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

$Z = \frac{54 - 53}{1.64}$

$Z = 0.61$

$Z = 0.61$ has a pvalue of 0.72907.

So, there is a 0.88877 - 0.72907 = 0.1597 = 15.97% probability that x will be between 54 and 55.

(c) Find the 47th percentile of x. Round the answer to at least two decimal places.

This is the value of X when Z has a pvalue of 0.47;

This is between $Z = -0.07$ and $Z = -0.08$ . So we use $Z = -0.075$ .

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

$-0.075 = \frac{X - 53}{1.64}$

$X = 52.877$

The 47th percentile of x is $X = 52.877$ .

8 0

3 years ago

Find the geometric mean between 4 and 1/4. Show your work.

Darya [45]

Answer:

2.125

Step-by-step explanation:

3 0

3 years ago

Pls help I will appreciate pls

Alex

Answer:

S = (1 times 5)times 6

Step-by-step explanation:

Question 5. Because there are 6 friends and each of them gets 5. one of them gets 5 But there are 6 friends so you multiply by 6. 6 times 5 is 30

6 0

3 years ago

Consider the curve defined by the equation y=6x2+14x. Set up an integral that represents the length of curve from the point (−2,

torisob [31]

Answer:

32.66 units

Step-by-step explanation:

We are given that

$y=6x^2+14x$

Point A=(-2,-4) and point B=(1,20)

Differentiate w.r. t x

$\frac{dy}{dx}=12x+14$

We know that length of curve

$s=\int_{a}^{b}\sqrt{1+(\frac{dy}{dx})^2}dx$

We have a=-2 and b=1

Using the formula

Length of curve= $s=\int_{-2}^{1}\sqrt{1+(12x+14)^2}dx$

Using substitution method

Substitute t=12x+14

Differentiate w.r t. x

$dt=12dx$

$dx=\frac{1}{12}dt$

Length of curve= $s=\frac{1}{12}\int_{-2}^{1}\sqrt{1+t^2}dt$

We know that

$\sqrt{x^2+a^2}dx=\frac{x\sqrt {x^2+a^2}}{2}+\frac{1}{2}\ln(x+\sqrt {x^2+a^2})+C$

By using the formula

Length of curve= $s=\frac{1}{12}[\frac{t}{2}\sqrt{1+t^2}+\frac{1}{2}ln(t+\sqrt{1+t^2})]^{1}_{-2}$

Length of curve= $s=\frac{1}{12}[\frac{12x+14}{2}\sqrt{1+(12x+14)^2}+\frac{1}{2}ln(12x+14+\sqrt{1+(12x+14)^2})]^{1}_{-2}$

Length of curve= $s=\frac{1}{12}(\frac{(12+14)\sqrt{1+(26)^2}}{2}+\frac{1}{2}ln(26+\sqrt{1+(26)^2})-\frac{12(-2)+14}{2}\sqrt{1+(-10)^2}-\frac{1}{2}ln(-10+\sqrt{1+(-10)^2})$