Mathematics, 30.11.2019 06:31 acamjackie25561

The random variable x is normally distributed with mean 5 and standard deviation 25. the random variable y is defined by y = 2 + 4x. what are the mean and the standard deviation of y ? the mean is 20 and the standard deviation is 102.
a) the mean is 20 and the standard deviation is 50.
b) the mean is 22 and the standard deviation is 102.
c) the mean is 22 and the standard deviation is 100.
d) the mean is 22 and the standard deviation is 50.

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Answer from: sierraaasifuent

C) The mean is 22 and the standard deviation is 100.

Step-by-step explanation:

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 expected value of a random variable X is the n-th moment about zero of a probability density function f(x) if X is continuous, or the weighted average for a discrete probability distribution, if X is discrete.

The variance of a random variable X represent the spread of the possible values of the variable. The variance of X is written as Var(X).

If $X\ sim N(\mu_x =5, \sigma_x =25)$

And the random variable Y =2+4X.

If we are interested in find the mean and the standard deviation for this new variable we need to apply the concepts of expected value and Variance of random variables.

Using the concept of expected value we have:

E(Y) =E(2+4X) = E(2) +E(4X)= 2+ 4E(X) =2+4(5) =2+20=22

So on this case the $E(Y) =\mu_Y =22$

Using the concept of variance we have:

Var(Y)=Var(2+4x)=Var(2)+Var(4X)+2Cov(2,4X)

But since 2 is a constant we don't have variance for this and the Cov(2,4x)=0 because the covariance of a random variable with a constant is zero. So applying these concepts we have:

$Var(Y)= Var(4x)=4^2 Var (X)= 16 \sigma^2_x =16(25^2)=10000$

And then if we need the standard deviation we just need to take the square root:

$sd(Y) = \sqrt{10000}=100$

So the best option for this case would be:

C) The mean is 22 and the standard deviation is 100.

Answer from: Quest

the ratio of white tiles to blue tiles is 48: 16. the ratio in it's simplest form is 3: 1.

step-by-step explanation:

ratio: take the first number and add a colon next to it, then add the second number after that. make sure the ratio order matches up with the written problem!

simplest form: we can simplify the ratio 48 : 16 by dividing both terms by the greatest common factor (gcf).

the gcf of 48 and 16 is 16.

divide both terms by 16:

48 ÷ 16 = 3

16 ÷ 16 = 1

reducing to simplest form:

48 : 16 = 3 : 1

Answer from: Quest

step-by-step explanation:

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