 jubateee

2021-12-28

Study the binomial distribution table. Notice that the probability of success on a single trial p ranges from 0.01 to 0.95. Some binomial distribution tables stop at 0.50 because of the symmetry in the table. Let's look for that symmetry. Consider the section of the table for which $n=5$. Look at the numbers in the columns headed by . Do you detect any similarities? Consider the following probabilities for a binomial experiment with five trials.
(a) Compare P(3 successes), where $p=0.30$, with , where $p=0.70$.
, where $p=0.30$, is larger. P(3 successes), where $p=0.30$, is smaller. They are the same.
(b) Compare P(3 or more successes), where $p=0.30$, with P(2 or fewer successes), where $p=0.70$.
P(3 or more successes), where $p=0.30$, is larger.P(3 or more successes), where $p=0.30$, is smaller. They are the same.
(c) Find the value of P(4 successes), where $p=0.30$. (Round your answer to three decimal places.)
For what value of r is P(r successes) the same using $p=0.70?$
$r=$ enhebrevz

Step 1
a) Given that $n=5$
Consider P(3 successes), if $p=0.30$

Consider P(2 or fewer successes), where $p=0.7$

Here, the value of P(3 successes) is less than P(2 or fewer successes).
P(3 successes), where $p=0.30$, is smaller than P(2 or fewer successes), where $p=0.70$.
Step 2
b) Given that $n=5$
Consider P(3 or more successes), if $p=0.30$

Consider P(2 or fewer successes), where $p=0.7$

$=\left(\begin{array}{c}5\\ 0\end{array}\right){0.7}^{0}\left(1-0.7{\right)}^{5-0}+\left(\begin{array}{c}5\\ 1\end{array}\right){0.7}^{1}\left(1-0.7{\right)}^{5-1}+\left(\begin{array}{c}5\\ 2\end{array}\right){0.7}^{2}\left(1-0.7{\right)}^{5-2}=0.1631$
Here, the value of P(3 or more successes) is same as P(2 or fewer successes).
P(3 or more successes), where $p=0.30$, is same as P(2 or fewer successes), where $p=0.70$.
Step 3
c) P(4 successes), where $p=0.30$. deginasiba

Step 1
a) From table:
where $p=0.30$ and $n=5$
, where $p=0.70$ and $n=5$
They are the same.
b) $P\left(3\text{or more successes}\right)=0.1323+0.0284+0.0024=0.1631,$ where $p=0.30$ and $n=5$
$P\left(3\text{or fewer successes}\right)=0.1323+0.0284+0.0024=0.1631,$ where $p=0.70$ and $n=5$
They are the same.
c) , where $p=0.30$ and $n=5$
, where $p=0.70$ and $n=5$
So, $r=1$
d) the column headed by $p=0.80$ karton