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Anna [14]
2 years ago
6

Suppose babies born in a large hospital have a mean weight of 4095 grams, and a standard deviation of 569 grams. If 130 babies a

re sampled at random from the hospital, what is the probability that the mean weight of the sample babies would differ from the population mean by greater than 42 grams? Round your answer to four decimal places.
Mathematics
1 answer:
Butoxors [25]2 years ago
6 0

Answer:

P =0.3998

Step-by-step explanation:

Let {\displaystyle {\overline{x}}} be the average of the sample, and the population mean will be \mu

We know that:

\mu = 4095 gr

Let \sigma be the standard deviation and n the sample size, then we know that the standard error of the sample is:

E=\frac{\sigma}{\sqrt{n}}

Where

\sigma=569

n=130

In this case we are looking for:

P(|{\displaystyle{\overline{x}}}- \mu|>42)

This is:

{\displaystyle{\overline{x}}}- \mu>42 or {\displaystyle{\overline{x}}}- \mu

P=P({\displaystyle{\overline{x}}}- \mu>42)+ P({\displaystyle{\overline{x}}}- \mu

Now we get the z score

Z=\frac{{\displaystyle{\overline{x}}}-\mu}{\frac{\sigma}{\sqrt{n}}}

P=P(z>\frac{42}{\frac{569}{\sqrt{130}}}) + P(z

P=P(z>0.8416) + P(z

Looking at the tables for the standard nominal distribution we get

P =0.1999+0.1999

P =0.3998

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liq [111]
Let's denote students in D = in the drama club , S<span> = in a sports team </span>
<span>P(D) = 85/330 </span>
<span>P(S) = 200/330 </span>
<span>
P(D and S) = 60/300 </span>
<span>
P(D or S) = P(D) + P(S) - P(D and S)  </span><span>= 85/330 + 200/330 - 60/330 = 15/22 </span>
<span>
P(neither D nor S) = 1- 15/22 </span><span>= 7/22</span>
7 0
2 years ago
Kaitlyn solved the equation for x using the following calculations. Negative 5.4 + x = 12.2. Minus 5.4. x = 6.8. What error, if
omeli [17]

Step-by-step explanation:

The equation that Kaitlyn solved is as follows :

-5.4+x=12.2

The steps to solve it as follows :

Step 1. Add 5.4 to both sides,

-5.4+x+5.4=12.2+5.4

Step 2. 5.4 will cancel out as both have opposite signs

x=17.6

But Kaitlyn solved it as :

5.4.x=6.8

She has multiplied -5.4 and x which is wrong. The correct answer is 17.6.

3 0
2 years ago
If ABCD is a square and AB = 10, what is the measure of CE to the nearest hundredth?
andrey2020 [161]

Answer:

AC=14.14\ units

Step-by-step explanation:

<em><u>The correct question is </u></em>

If ABCD is a square and AB = 10, what is the measure of AC? (rounded to the nearest hundredth)

see the attached figure to better understand the problem

we know that

All four sides of the square are congruent and all four interior angles are equal to 90°.

so

AB=BC=CD=AD

In the right triangle ACD

Applying the Pythagorean Theorem

AC^2=CD^2+AD^2

we have that

CD=AD=AB=10\ units

substitute the given value

AC^2=10^2+10^2

AC^2=200

AC=\sqrt{200}\ units

AC=14.14\ units

6 0
2 years ago
Use complete sentences to describe the transformation that maps ABCD onto its image.
Lapatulllka [165]

General Idea:

When a point or figure on a coordinate plane is moved by sliding it to the right or left or up or down, the movement is called a translation.

Say a point P(x, y) moves up or down ' k ' units, then we can represent that transformation by adding or subtracting respectively 'k' unit to the y-coordinate of the point P.

In the same way if P(x, y) moves right or left ' h ' units, then we can represent that transformation by adding or subtracting respectively 'h' units to the x-coordinate.

P(x, y) becomes P'(x\pm h, y\pm k). We need to use ' + ' sign for 'up' or 'right' translation and use ' - ' sign for ' down' or 'left' translation.

Applying the concept:

The point A of Pre-image is (0, 0). And the point A' of image after translation is (5, 2). We can notice that all the points from the pre-image moves 'UP' 2 units and 'RIGHT' 5 units.

Conclusion:

The transformation that maps ABCD onto its image is translation given by (x + 5, y + 2),

In other words, we can say ABCD is translated 5 units RIGHT and 2 units UP to get to A'B'C'D'.

6 0
2 years ago
In a day, Robin spends 6 hours at school, sleeps for 9 hours, plays for 3 hours, and spends the rest of the time doing other thi
slavikrds [6]
6hrs = school
9hrs = sleeps              = 18hrs // 24hrs      ----6hrs left
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6hrs = other things


playing = 12.5% -- 3/24                 3/24*100
other things = 25% -- 6/24             6/24*100
5 0
2 years ago
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