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2 years ago

Compute the standard deviation of the following set of data to the nearest whole number:

Mathematics

1 answer:

Klio2033 [76]2 years ago

3 0

Answer:

Step-by-step explanation:

The standard deviation is the square root of the variance, and the variance is found by using the mean. So we will do that first. I will use the population variance as opposed to the sample variance since our set of numbers is small.

The mean: 8 + 12 + 15 + 17 + 18 = 70 and divide that by 5 to get

$\bar{x}=14$ and use this to find the variance in the formula:

$s^2=\frac{\sum(x_i-\bar{x})^2}{n}$ it is a bit difficult to enter that formula in correctly, but here's how it works mathematically:

$s^2=\frac{(8-14)^2+(12-14)^2+(15-14)^2+(17-14)^2+(18-14)^2}{5}$

Squaring this ensures us that we don't end up with zero, which would be useless.

$s^2=\frac{36+4+1+9+16}{5}$ so

$s^2=13.2$ which means that the standard deviation is

s = 3.633

(If you do it with n-1 = 4 in the denominator of the variance, you get a standard deviation of 4.062)

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Maggie is practicing her penalty kicks for her upcoming soccer game. During the practice, she attempts 10 penalty kicks. If each

arlik [135]

Answer:

$P(X \geq 8)= P(X=8) +P(X=9) +P(X=10)$

And we can find the individual probabilities like this:

$P(X=8)=(10C8)(0.65)^0 (1-0.65)^{10-8}=0.176$

$P(X=9)=(10C9)(0.65)^1 (1-0.65)^{10-9}=0.072$

$P(X=10)=(10C10)(0.65)^2 (1-0.65)^{10-10}=0.013$

And adding we got:

$P(X \geq 8)= P(X=8) +P(X=9) +P(X=10)= 0.176+0.072+0.013=0.262$

Step-by-step explanation:

Previous concepts

The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".

Let X the random variable of interest, on this case we now that:

$X \sim Binom(n=10, p=0.65)$

The probability mass function for the Binomial distribution is given as:

$P(X)=(nCx)(p)^x (1-p)^{n-x}$

Where (nCx) means combinatory and it's given by this formula:

$nCx=\frac{n!}{(n-x)! x!}$

Solution to the problem

For this case we want to find this probability:

$P(X \geq 8)= P(X=8) +P(X=9) +P(X=10)$

And we can find the individual probabilities like this:

$P(X=8)=(10C8)(0.65)^0 (1-0.65)^{10-8}=0.176$

$P(X=9)=(10C9)(0.65)^1 (1-0.65)^{10-9}=0.072$

$P(X=10)=(10C10)(0.65)^2 (1-0.65)^{10-10}=0.013$

And adding we got:

$P(X \geq 8)= P(X=8) +P(X=9) +P(X=10)= 0.176+0.072+0.013=0.262$

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What will be the product if a number if it is multiplied by 1?

Amanda [17]

The product if a number if it is multiplied by 1 is the same number itself.

Given:

Product:

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Learn more about the number here:

brainly.com/question/17429689

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