Question

g red bell pepper seeds germinates 85% of the time. planted 25 seeds. What is the probability that 20 or more germinate

Answer 1

Answer:

$P(X\geq 20)= P(X=20)+P(X=21)+P(X=22)+P(X=23)+P(X=24)+P(X=25)$

And replacing using the mass function we got:

$P(X=20)=(25C20)(0.85)^{20} (1-0.85)^{25-20}=0.156$  

$P(X=21)=(25C21)(0.85)^{21} (1-0.85)^{25-21}=0.211$  

$P(X=22)=(25C22)(0.85)^{22} (1-0.85)^{25-22}=0.217$  

$P(X=23)=(25C23)(0.85)^{23} (1-0.85)^{25-23}=0.161$  

$P(X=24)=(25C24)(0.85)^{24} (1-0.85)^{25-24}=0.0759$  

$P(X=25)=(25C25)(0.85)^{25} (1-0.85)^{25-25}=0.0172$  

And adding the values we got:

$P(X\geq 20) = 0.8381$

Step-by-step explanation:

Let X the random variable of interest, on this case we now that:  

$X \sim Binom(n=25, p=0.85)$  

The probability mass function for the Binomial distribution is given as:  

$P(X)=(nCx)(p)^x (1-p)^{n-x}$  

Where (nCx) means combinatory and it's given by this formula:  

$nCx=\frac{n!}{(n-x)! x!}$  

We want to find the following probability:

$P(X\geq 20)= P(X=20)+P(X=21)+P(X=22)+P(X=23)+P(X=24)+P(X=25)$

And replacing using the mass function we got:

$P(X=20)=(25C20)(0.85)^{20} (1-0.85)^{25-20}=0.156$  

$P(X=21)=(25C21)(0.85)^{21} (1-0.85)^{25-21}=0.211$  

$P(X=22)=(25C22)(0.85)^{22} (1-0.85)^{25-22}=0.217$  

$P(X=23)=(25C23)(0.85)^{23} (1-0.85)^{25-23}=0.161$  

$P(X=24)=(25C24)(0.85)^{24} (1-0.85)^{25-24}=0.0759$  

$P(X=25)=(25C25)(0.85)^{25} (1-0.85)^{25-25}=0.0172$  

And adding the values we got:

$P(X\geq 20) = 0.8381$