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Assume the random variable X has a binomial distribution with the given probability of obtaining a success. Find the following probability, given the number of trials and the probability of obtaining a success . Round your answer to four decimal places. ${\displaystyle P\left(X<4\right),n=6,p=0.4}$

Eighty percent of households say they would feel secure if they had 50,000 in savings. You randomly select 8 households and ask them if they would feel secure if they had $50,000 in savings. Find the probability that the number that say they would feel secure is exactly five, (b) more than five, and (c) at most five
c.) Find the probability that the number that say they would feel secure is at most five. ${\displaystyle P\left(<5\right)=}$
(round to three decimal places as needed).

Your friend is attempting 10 free throws, and from experience, you know that your friend’s probability of scoring a free throw is 0.7. What is the probability that your friend would score 8 free throws ?

Assume that a procedure yields a binomial distribution with a trial repeated ${\displaystyle n=5}$ times. Use some form of technology to find the cumulative probability distribution given the probability ${\displaystyle p=0.16}$ of success on a single trial.
(Report answers accurate to 4 decimal places.)
$\begin{array}{|cc|}\hline k& P(X=k)\\ 0& \\ 1& \\ 2& \\ 3& \\ 4& \\ 5& \\ \hline\end{array}$

X denotes a binomial random variable with parameters n and p, Indicate which area under the appropriate normal curve would be determined to approximate the specified binomial probability.
${\displaystyle P\left(X<4\right)}$

Assume that X is an ${\displaystyle n=200\text{and}p=0.3}$ dimensional binomial random variable. Estimate the likelihood that ${\displaystyle X=80}$. When using the Binomial distribution technique, compare this outcome. What judgment do you make?