A population of values has a normal distribution with \mu = 116.5 and \sigma = 63.7. You intend to draw a random sample of size n = 244.

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 ${\displaystyle \mu =133.5}$ 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.

What is a discrete probability distribution? What two conditions determine a probability distribution?

For a population with a mean of ${\displaystyle \mu =100}$ and a standard deviation of ${\displaystyle \sigma =20}$,
Find the X values.
${\displaystyle z=+.75}$.

You have studied the number of people waiting in line at your bank on Friday afternoon at 3 pm for many years, and have created a probability distribution for 0, 1, 2, 3, or 4 people in line. The probabilities are 0.1, 0.3, 0.4, 0.1, and 0.1, respectively. What is the expected number of people (mean) waiting in line at 3 pm on Friday afternoon?

Suppose that the random variables X and Y have joint p.d.f.
$f(x,y)=\{\begin{array}{l}kx(x-y),\\ 0\end{array}$

Evaluate the constant k.

If the joint probability density function of two continuous random variables X and Y isgiven by f(x; y) = 2, 0 < y < 3x, 0 < x < 1;find,(a) f(y/x),(b) E(Y/x), (c) Var(Y/x).