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sweet-ann [11.9K]
3 years ago
7

A study indicates that 37% of students have laptops. You randomly sample 30 students. Find the mean and the standard deviation o

f the number of students with laptops.
Mathematics
1 answer:
Brilliant_brown [7]3 years ago
5 0

Answer:

The mean and the standard deviation of the number of students with laptops are 1.11 and 0.836 respectively.

Step-by-step explanation:

Let <em>X</em> = number of students who have laptops.

The probability of a student having a laptop is, P (X) = <em>p</em> = 0.37.

A random sample of <em>n</em> = 30 students is selected.

The event of a student having a laptop is independent of the other students.

The random variable <em>X</em> follows a Binomial distribution with parameters <em>n</em> and <em>p</em>.

The mean and standard deviation of a binomial random variable <em>X</em> are:

\mu=np\\\sigma=\sqrt{np(1-p)}

Compute the mean of the random variable <em>X</em> as follows:

\mu=np=30\times0.37=1.11

The mean of the random variable <em>X</em> is 1.11.

Compute the standard deviation of the random variable <em>X</em> as follows:

\sigma=\sqrt{np(1-p)}=\sqrt{30\times0.37\times(1-0.37)}=\sqrt{0.6993}=0.836

The standard deviation of the random variable <em>X</em> is 0.836.

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Which of the following is most likely the next step in the series?<br> B
iVinArrow [24]

Answer:

C

Step-by-step explanation:

The pattern seems to go as follows:

1. Top left portion is in blue

2. Top left portion is in blue as well as the rest of the upper half filled with red.

3. Another portion of blue is added directly underneath the red.

This leads me to believe that the colors are alternating from blue to red to blue to finally, red. This makes your answer C. Please let me know if you still need help!

3 0
2 years ago
Read 2 more answers
Which of the following options have the same value as %5, percent of 35? Choose 2 answers: (Choice A) A 5*35 (Choice B) B 5/100*
nasty-shy [4]

Answer:

B and D

Step-by-step explanation:

5% of 35 can be represented as 5% \cdot35.

To find equations that make this work, we need to find different ways to represent 5%.

5% can be represented as fraction - over 100. The percentage over 100 will be equal to the percent.

So, \frac{5}{100}. Multiplying by 35 gets us \frac{5}{100}\cdot35

This means that Choice B is correct.

Another way to represent 5% is as a decimal.

We already know that the fraction form of 5% is \frac{5}{100}. This means that in the decimal, the number 5 will be two place values to the right of the decimal place.

0.<u>0</u><u>5</u>

So the decimal expansion of 5% is 0.05. Multiplyin by 35 get us 0.05\cdot35, so choice D works too.

Hope this helped!

3 0
3 years ago
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Chase has 3 gallons of a solution that is 30% antifeeze that he wants to use to winterize his car. How much pure antifreeze shou
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There are 30% of pure antifreeze in 3 gallons of solution, then

3 gallons - 100%,

a gallons - 30%,

where a gallons is the amount of pure antifreeze in given solution.

Mathematically,

\dfrac{3}{a}=\dfrac{100}{30},\\ \\a=\dfrac{3\cdot 30}{100}=0.9\ gallons.

Now in new solution there will be x+0.9 gallons of pure antefreeze.

x+3 gallons - 100%,

x+0.9 - 65%

or

\dfrac{x+3}{x+0.9}=\dfrac{100}{65},\\ \\65(x+3)=100(x+0.9),\\ \\65x+195=100x+90,\\ \\35x=105,\\ \\x=3\ gallons.

Answer: he should add 3 gallons of pure antifreeze.

8 0
3 years ago
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