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In Exercises, X denotes a binomial random variable with parameters n and p. For each exercise, indicate which area under the appropriate normal curve would be determined to approximate the specified binomial probability.
${\displaystyle P\left(7<X<10\right)}$

What value of p will give the following probability distribution if x is Binomially distributed with ${\displaystyle n=5}$ and probability of success p? 
$\begin{array}{|ccccccc|}\hline x& 0& 1& 2& 3& 4& 5\\ P\left(x\right)& 0.0916& 0.2808& 0.3441& 0.2109& 0.0646& 0.0079\\ \hline\end{array}$ 
Group of answer choices 30% 32% 34% 36% 38%

Assuming a procedure results in a binomial distribution with ${\displaystyle n=7}$ trials and a probability of success of ${\displaystyle p=0.90}$. Use a binomial probability table to find the probability that the number of successes x is exactly three.
${\displaystyle P\left(3\right)=?}$ (round to three decimal places as needed)

Assume that a procedure yields a binomial distribution with a trial repeated $n=5$ times. Use some form of technology to find the probability distribution given the probability $p=0.413$ of success on a single trial. 
(Report answers accurate to 4 decimal places.) 
$\begin{array}{|cc|}\hline k& P(X=k)\\ 0& \\ 1& \\ 2& \\ 3& \\ 4& \\ 5& \\ \hline\end{array}$

The variance for the binomial probability distribution is
1) ~$(x)=P(1-P)$
2) ~$(x)=nP$
3) ~$(x)=n(1-P)$
4) ~$(x)=nP(1-P)$

Compute the probability of x successes in the n independent trials of the binomial experiment. 
${\displaystyle n=10,p=0.6,x=7}$ 
${\displaystyle P\left(7\right)=?}$

Calculate the likelihood that X will succeed using Table B in appendix A.
a. ${\displaystyle n=15,p=0.80,X=12}$ 
b. ${\displaystyle n=20,p=0.05,X=0}$ 
c. ${\displaystyle n=20,p=0.50,X=10}$ 
d. ${\displaystyle n=16,p=0.20,X=3}$

Assume that a procedure yields a binomial distribution with a trial repeated $n=5$ times. Use some form of technology to find the probability distribution given the probability $p=0.6$ of success on a single trial. 
(Report answers accurate to 2 decimal places.) 
$\begin{array}{|cc|}\hline k& P(X=k)\\ 0& \\ 1& \\ 2& \\ 3& \\ 4& \\ 5& \\ \hline\end{array}$