A distribution of values is normal with a mean of 166.1 and a standard deviation of 73.5.Find the probability that a randomly selected value is between 151.4 and 283.7.P(151.4 < X < 283.7) = IncorrectWrite 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 ${\displaystyle \mu =133.5}$ 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.

Let ${\displaystyle X_1,X_2,\dots ,X_6}$ be an i.i.d. random sample where each ${\displaystyle X_i}$ is a continuous random variable with probability density function
${\displaystyle f\left(x\right)=e^{-(x-0)},x>0}$
Find the probability density function for ${\displaystyle X_6}$.

A population has a mean of 24.8 and a standard deviation of 4.2. If ${\displaystyle x_i=19}$, what is the z-value?

Suppose that you get into a car accident at an average rate of about one accident every 3 years. In the next 21 years, you would expect to have about 7 accidents. if you actually had 5 accidents in that time, can you say that you're a better driver?

The amount of cereal that can be poured into a small bowl varies with a mean of 1.5 ounces and a standard deviation of 0.3 ounces. A large bowl holds a mean of 2.5 ounces with a standard deviation of 0.4 ounces. You open a new box of cereal and pour one large and one small bowl. a) How much more cereal do you expect to be in the large bowl? b) What 's the standard deviation of this difference? c) If the difference follows a Normal model, what's the probability the small bowl contains more cereal than the large one? d) What are the mean and standard deviation of the total amount of cereal in the two bowls? e) If the total follows a Normal model, what's the probability you poured out more than 4.5 ounces of cereal in the two bowls together? f) The amount of cereal the manufacturer puts in the boxes is a random variable with a mean of 16.3 ounces and a standard deviation of 0.2 ounces. Find the expected amount of cereal left in the box and the standard deviation.

Random variables X and Y have joint PDF
$f_{X,Y}(x,y)=\{\begin{array}{l}12e^{-(3x+4y)},x\ge 0,y\ge 0\\ 0,otherwise\end{array}$
Find $P[max(X,Y)\le 0.5]$