Solve for the value of X

Compute each probability. The strategy is to transform X, a random variable representing the weight of newborns, to another random variable Z that represents the same but scaled quantity so that Z is normally distributed with mean 0 and s.d. 1. To do this, we use the rule

X = 5.5 + 1.6 Z

or

Z = (X - 5.5)/1.6

then use a calculator to compute the probability, or look it up in a table. Multiply this probability by 800 to find the number of newborns in each category.

1.

Pr[3 ≤ X ≤ 8] = Pr[(3 - 5.5)/1.6 ≤ (X - 5.5)/1.6 ≤ (8 - 5.5)/1.6]

… ≈ Pr[-1.5625 ≤ Z ≤ 1.5625]

… ≈ 0.8818

Out of 800 babies, you would expect around 88% of them, or about 705 babies to weight between 3 and 8 pounds.

2.

Pr[X < 6] = Pr[(X - 5.5)/1.6 ≤ (6 - 5.5)/1.6]

… = Pr[Z ≤ 0.3125]

… ≈ 0.6227

Out of 800 babies, around 498 will weigh less than 6 pounds.

3.

Pr[X > 5] = Pr[(X - 5.5)/1.6 > (5 - 5.5)/1.6]

… = Pr[Z > -0.3125]

… ≈ 0.6227

same as (2) due to the symmetry of the distribution (Z is centered at zero). Out of 800 babies, you can expect around 498 in this group.

4.

Pr[5.5 ≤ X ≤ 9] = Pr[(5.5 - 5.5)/1.6 ≤ (X - 5.5)/1.6 ≤ (9 - 5.5)/1.6]

… = Pr[0 ≤ Z ≤ 2.1875]

… ≈ 0.4857

Out of 800 babies, around 388 will weigh between 5.5 and 9 pounds.

The standard deviation of the grade points average of the college seniors is 0.57.

The given parameters:

3.2, 1.9 ,2.7, 2.4, 2.8, 2.9, 3.8, 3.0, 2.5, 3.3, 1.8, 2.5, 3.7, 2.8, 2.0, 3.2, 2.3, 2.1, 2.5, 1.9

The sum of the given data is calculated as follows;

∑x = 3.2 + 1.9 + 2.7 +  2.4 + 2.8 + 2.9 + 3.8 + 3.0 +  2.5 + 3.3 + 1.8 + 2.5 + 3.7 + 2.8 + 2.0 + 3.2 + 2.3 + 2.1 + 2.5 + 1.9

∑x = 53.3

The mean of the distribution is calculated as follows;

[tex]\bar x = \frac{\Sigma x}{N} \\\\\bar x = \frac{53.3}{20} \\\\\bar x = 2.665[/tex]

The square of the difference between the grade point and the mean;

[tex]\Sigma (x - \bar x)^2 = (3.2- 2.665)^2 + (1.9-2.665)^2 + (2.7- 2.665)^2 + (2.4-2.665)^2 \\\\+(2.8-2.665)^2 +(2.9 - 2.665)^2 + (3.8 - 2.665)^2 + (3-2.665)^2+ \\\\(2.5 -2.665)^2 + (3.3 - 2.665)^2 + (1.8-2.665)^2 + (2.5 - 2.665)^2 + \\\\(3.7-2.665)^2 + (2.8 - 2.665)^2 + (2-2.665)^2 + (3.2-2.665)^2 + \\\\(2.3 - 2.665)^2 + (2.1-2.665)^2 + (2.5-2.665)^2 + (1.9 - 2.665)^2\\\\\Sigma (x - \bar x)^2 = 6.5055[/tex]

The standard deviation of the grade points is calculated as follows;

[tex]\sigma = \sqrt{\frac{\Sigma (x-\bar x)^2}{N} } \\\\\sigma = \sqrt{\frac{6.5055}{20} } \\\\\sigma = 0.57[/tex]

Thus, the standard deviation of the grade points average of the college seniors is 0.57.

Learn more about standard deviation here: https://brainly.com/question/12402189

Answer:

                                 pop

                                             yes                   no             total

country            yes                  11                      38              49

                        no                       43                     8                51

                         total                54                     46               100

Hope you understand this haha

The answer is in the file. Hope it helps.

Answer:

7

Step-by-step explanation:

1/3*(-18) + 1 = 7

Just plug in the x which is -18, and solve with a calculator.

Hope this helps!

Answer:

B is empty

Step-by-step explanation:

Answer:

[tex]x=-\frac{1}{2}[/tex] and [tex]x=-2[/tex]

Step-by-step explanation:

[tex]f(x)=\frac{2x^2+5x+2}{x^2-4x+3}[/tex]

[tex]0=\frac{2x^2+5x+2}{x^2-4x+3}[/tex]

[tex]0=\frac{(2x+1)(x+2)}{(x-1)(x-3)}[/tex]

[tex]0=(2x+1)(x+2)[/tex]

[tex]2x+1=0[/tex] and [tex]x+2=0[/tex]

[tex]x=-\frac{1}{2}[/tex] and [tex]x=-2[/tex]

Given terms in an AP are √2,√8,√18

√8 = √(2×2×2) = 2√2

√18 = √(2×3×3) = 3√2

The AP : √2,2√2,3√2

next term = 4√2> √(4×4×2)

⇛ √32

The next term of the AP = √32.

also read similar questions: The next term of the AP root 8, root 18,root 32 is...........

https://brainly.com/question/17287744?referrer

Which term of the AP:3, 8, 13, 18,...,is 78?

https://brainly.com/question/15380012?referrer

Answer:

45+x = 71

26 players were added

Step-by-step explanation:

We start with 45 players

We ended with 71 players

We added x players

45+x = 71

Subtract 45 from each side

45+x-45 = 71-45

x =26

We added 26 players

ATQ

[tex]\\ \sf{:}\dashrightarrow x+45=71[/tex]

[tex]\\ \sf{:}\dashrightarrow x=71-45[/tex]

[tex]\\ \sf{:}\dashrightarrow x=26[/tex]

Answer:

x=61

Step-by-step explanation:

2x-6+x+3=180

3x-3=180

3x=183

x= 61

I have no clue I just need the points have a good day tho :)

Answer:

t^7

Step-by-step explanation:

there are 7 ts so it is t to the power of 7

Answer:

000

Step-by-step explanation:

000

Answer:

[tex]$\lim_{x\to 0^+} \tan(x) - \frac{1}{x^2} = -\infty$[/tex]

Step-by-step explanation:

[tex]$\lim_{x\to 0^+} \tan(x) - \frac{1}{x^2} = \lim_{x\to 0^+} \tan(x) - \lim_{x\to 0^+} \frac{1}{x^2} $[/tex]

and

[tex]$\lim_{x\to 0^+} \tan(x) = \tan(0) = 0$[/tex]

[tex]$\lim_{x\to 0^+} \frac{1}{x^2} = +\infty$[/tex]

Therefore,

[tex]$\lim_{x\to 0^+} \tan(x) - \frac{1}{x^2} = -\infty$[/tex]

Answer:

A

Step-by-step explanation:

Did the test

Answer:

12.4 ft

Step-by-step explanation:

Everything is done right so far.

Now to calculate the height of the tree, 12tan46, put the equation into a calculator.

Either a graphing calculator (make sure it is in degrees, not radians),

or the one on your phone (turn your phone landscape in the calculator app to get the trig functions.))

12tan46= 12.4 ft

Answer:

y < 1

Step-by-step explanation:

In order to solve this inequality, we must isolate the y variable.

First add 5 on both sides of the inequality sign:

Now you have 8y < 8.

Then divide by 8 on both sides, to get y alone:

Now you have y < 1.

Hope this helps you :)

Answer:

g(x) = (5x + 3)/ x - 7

Step-by-step explanation:

Let g(x) = y

y = (7x + 3)/x - 5

Make x the subject

xy - 5y = 7x + 3

xy - 7x = 5y + 3

x(y - 7) = 5y + 3

x = (5y + 3)/ y - 7

Therefore, the inverse of the function = (5x + 3)/ x - 7

Answer:

3 liters

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

x>−15/2

15/2 is a fraction

Step-by-step explanation:

is it like this ? no diagrams ?

Answer:

53.73

Step-by-step explanation:

Answer:

Im thinking its y=-2x but Im not 100% sorry if its wrong

Answer:

Step-by-step explanation:

Let x represent the amount invested at the higher rate. Then 1000-x is the amount invested at the lower rate. The total earnings are ...

  0.05(1000-x) +0.06x = 58

  50 +0.01x = 58 . . . . . . . . . . . simplify

  0.01x = 8 . . . . . . . . . . . . . . . subtract 50

  x = 800 . . . . . . . . . . . . . . . multiply by 100; amount at 6%

  (1000-x) = 200 . . . . . . . find the amount invested at 5%

Lara invested $200 at 5% and $800 at 6%.

A. AC≅AC, Reflexive Property of Congruence

Correct. This is shared side of the triangles ABC and CDA

B. ∠ACB≅∠CAD, Alternate Interior Angles Theorem

Correct. BC and AD are parallel and AC is transversal

C. ∠BAC≅∠DCA, Alternate Interior Angles Theorem

Correct. AB and DC are parallel and AC is transversal

D. △ABC≅△CDA, SAS Triangle Congruence Theorem

Incorrect. This should be ASA as we have shown above the angles A and C and included side AC are congruent.

Answer:

The first two entries are correct since they are given. Unless you make a mistake compliling the first cell in a "given" line, they are always correct

Third one is not: they are not angles. They are segments - technically they are the SAME segment, it's in common between the two triangles.

Last one is correct, it's SSA