A population of values has a normal distribution with \mu = 216.9 and \sigma = 87.1. You intend to draw a random sample of size n = 97.Find the probability that a single randomly selected value is between 193 and 244.3.P(193<X<244.3) =?Write your answers as numbers accurate to 4 decimal places.

A population of values has a normal distribution with ${\displaystyle \mu =133.5}$ and ${\displaystyle \sigma =5.2}$. You intend to draw a random sample of size ${\displaystyle n=230}$.
Find the probability that a single randomly selected value is between 133.6 and 134.1.
${\displaystyle P\left(133.6<X<134.1\right)=}$?
Write your answers as numbers accurate to 4 decimal places.

We wish to estimate what percent of adult residents in a certain county are parents. Out of 600 adult residents sampled, 192 had kids. Based on this, plot a $99\mathrm{\%}$ confidence interval for the proportion of adult residents who are parents in a given county.
Express your answer in the form of three inequalities. Give your answers in decimal fractions up to three places ${\displaystyle <p<}$ Express the same answer using a point estimate and a margin of error. Give your answers as decimals, to three places.
${\displaystyle p=\pm }$

A population of values has a normal distribution with ${\displaystyle \mu =239.5}$ and ${\displaystyle \sigma =32.7}$. You intend to draw a random sample of size ${\displaystyle n=139}$.
Find the probability that a sample of size $n=139$ is randomly selected with a mean greater than 235.9.
${\displaystyle P\left(M>235.9\right)=}$?
Write your answers as numbers accurate to 4 decimal places.

For continuous random variables X and Y with joint probability density function
$f(x,y)=\{\begin{array}{ll}x{e}^{-(x+xy)}& x>0andy>0\\ 0& otherwise\end{array}$
Are X and Y independent? Explain.

Consider two continuous random variables X and Y with joint density function
${\displaystyle f(x,y)=beg\in \left\{cases\right\}x+yo\le x\le 1,0\le y\le 1\mathrm{\setminus }0otherwiseend\left\{cases\right\}}$
P(X>0.8, Y>0.8) is?

The number of surface flaws in a plastic roll used in the interior of automobiles has a Poisson distribution with a mean of 0.06 flaw per square foot of plastic roll. What is the probability that there are no surface flaws in an auto’s interior?

What are the mean and standard deviation of a binomial probability distribution with n=130 and ${\displaystyle p=\frac{3}{4}}$?