The random variable X follows a normal distribution ?(20, 102). Find Find P(? > 30 ),

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 ${\displaystyle \mu =200.7}$ and ${\displaystyle \sigma =10}$. You intend to draw a random sample of size ${\displaystyle n=178}$
Find the probability that a sample of size ${\displaystyle n=178}$ is randomly selected with a mean less than 198.6.
${\displaystyle P\left(M<198.6\right)=}$?

A population of values has a normal distribution with ${\displaystyle \mu =221.6}$ and ${\displaystyle \sigma =44.1}$. You intend to draw a random sample of size $n=42$.
Find the probability that a single randomly selected value is between 221.6 and 229.1.
${\displaystyle P\left(221.6<X<229.1\right)=}$?
Write your answers as numbers accurate to 4 decimal places.

CNNBC recently reported that the mean annual cost of auto insurance is 954 dollars. Assume the standard deviation is 271 dollars. You take a simple random sample of 96 auto insurance policies.
Find the probability that a single randomly selected value is less than 969 dollars.
${\displaystyle P\left(x<969\right)=P\left(x<969\right)=}$?

Write your answers as numbers accurate to 4 decimal places.