PLEASE HELP‼️‼️<br> A<br> B<br> C<br> D

alexandr1967 [171]

Answer:

a) $P( X$

We want this probability:

$P( X >64)$

And using the z score formula given by:

$z = \frac{x -\mu}{\sigma}$

We got:

$P( X >64) =P(Z> \frac{64-42}{5.5}) =P(Z>4)=0.0000316$

b) For this part we want to find a value a, such that we satisfy this condition:

$P(X>a)=0.25$ (a)

$P(X$ (b)

Both conditions are equivalent on this case. We can use the z score again in order to find the value a.

As we can see on the figure attached the z value that satisfy the condition with 0.75 of the area on the left and 0.25 of the area on the right it's z=0.674. On this case P(Z<0.674)=0.75 and P(z>0.674)=0.25

If we use condition (b) from previous we have this:

$P(X$

$P(z$

But we know which value of z satisfy the previous equation so then we can do this:

$z=0.674$

And if we solve for a we got

$a=42 +0.674*5.5=45.707$

So the value of height that separates the bottom 75% of data from the top 25% is 45.707.

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".

Part a

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

$X \sim N(42,25.5)$

Where $\mu=42$ and $\sigma=5.5$

And we want this probability:

$P( X$

And using the z score formula given by:

$z = \frac{x -\mu}{\sigma}$

We got:

$P( X$

We want this probability:

$P( X >64)$

And using the z score formula given by:

$z = \frac{x -\mu}{\sigma}$

We got:

$P( X >64) =P(Z> \frac{64-42}{5.5}) =P(Z>4)=0.0000316$

Part b

For this part we want to find a value a, such that we satisfy this condition:

$P(X>a)=0.25$ (a)

$P(X$ (b)

Both conditions are equivalent on this case. We can use the z score again in order to find the value a.

As we can see on the figure attached the z value that satisfy the condition with 0.75 of the area on the left and 0.25 of the area on the right it's z=0.674. On this case P(Z<0.674)=0.75 and P(z>0.674)=0.25

If we use condition (b) from previous we have this:

$P(X$

$P(z$

But we know which value of z satisfy the previous equation so then we can do this:

$z=0.674$

And if we solve for a we got

$a=42 +0.674*5.5=45.707$

So the value of height that separates the bottom 75% of data from the top 25% is 45.707.

8 0

3 years ago

During the early part of the 1994 baseball season, many sports fans and baseball players noticed that the number of home runs be

natta225 [31]

Complete Question

The picture of the stem plot National and American League is shown on the first uploaded image

Answer:

The value is $\= x = 50.14$

Step-by-step explanation:

From the question we are told that

The stem plot for National League is

$2\ \ \ \ \ 9\\3\ \ \ \ \ 1 \\4\ \ \ \ \ 2\ 6\ 7\ 8\ 8\\5 \ \ \ \ \ 3\ 5\ 5\ 5\\6 \ \ \ \ \ 3\ 3\ 7\\7$

The sample size is n = 14

Generally the stem plot is interpreted in this manner

The numbers on the first column represents the tens of a two digit number while the second column holds the possible unit number the tens in the first column can be combined with

for example 4th row

5 3 5 5 5

is equivalent to

53 55 55 55

Generally the mean for the national league is mathematically represented as

$\= x = \frac{29 + 31 + \cdots + 67}{14}$

=> $\= x = \frac{702}{14}$

=> $\= x = 50.14$

4 0

3 years ago

Slope of the line that passes through (3, -11) and (0, 4), please!

Lorico [155]

Answer:

-5

Step-by-step explanation:

slope formula= $\frac{y1 - y2}{x1 - x2}$

slope of line

$= \frac{4 - ( - 11)}{0 - 3} \\ = \frac{4 + 11}{ - 3} \\ = \frac{15}{ - 3} \\ = - 5$

6 0

3 years ago

Determine the values of xfor which the function can be replaced by the Taylor polynomial if the error cannot exceed 0.001.(Enter

MrMuchimi

Answer:

The values of x for which the function can be replaced by the Taylor polynomial if the error cannot exceed 0.001 is 0 < x < 0.3936.

Step-by-step explanation:

Note: This question is not complete. The complete question is therefore provided before answering the question as follows:

Determine the values of x for which the function can be replaced by the Taylor polynomial if the error cannot exceed 0.001. f(x) = e^x ≈ 1 + x + x²/2! + x³/3!, x < 0

The explanation of the answer is now provided as follows:

Given:

f(x) = e^x ≈ 1 + x + x²/2! + x³/3!, x < 0 …………….. (1)

$R_{3}$ = (x) = (e^z /4!)x^4

Since the aim is $R_{3}$ (x) < 0.001, this implies that:

(e^z /4!)x^4 < 0.0001 ………………………………….. (2)

Multiply both sided of equation (2) by (1), we have:

e^4x^4 < 0.024 ……………………….......……………. (4)

Taking 4th root of both sided of equation (4), we have:

|xe^(z/4) < 0.3936 ……………………..........…………(5)

Dividing both sides of equation (5) by e^(z/4) gives us:

|x| < 0.3936 / e^(z/4) ……………….................…… (6)

In equation (6), when z > 0, e^(z/4) > 1. Therefore, we have:

|x| < 0.3936 -----> 0 < x < 0.3936

Therefore, the values of x for which the function can be replaced by the Taylor polynomial if the error cannot exceed 0.001 is 0 < x < 0.3936.

3 0

3 years ago

Which point has coordinates (4.9,3.9)

weqwewe [10]

Point C is the answer

8 0

3 years ago

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PLEASE HELP‼️‼️ A B C D