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jeyben [28]
3 years ago
6

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

Mathematics
1 answer:
bixtya [17]3 years ago
7 0

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

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Determine the first four terms of the sequence in which the nth term is a_n=(n+1)!/(n+2)!
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Answer: Choice B) 1/3, 1/4, 1/5, 1/6

=============================================

Plug in n = 1 to find the first term

a_n = ( (n+1)! )/( (n+2)! )

a_1 = ( (1+1)! )/( (1+2)! )

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The first term is 1/3. Optionally you can stop here because only choice B has 1/3 listed as the first term, so this must be the answer. However, I'm going to keep going to show how to find the three other terms. This will help confirm why choice B is the answer, and it will be handy for those times when you aren't given multiple choice answers.

------------

Plug in n = 2

a_n = ( (n+1)! )/( (n+2)! )

a_2 = ( (2+1)! )/( (2+2)! )

a_2 = ( 3! )/( 4! )

a_2 = ( 3*2*1 )/( 4*3*2*1 )

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The second term is 1/4

------------

Plug in n = 3

a_n = ( (n+1)! )/( (n+2)! )

a_3 = ( (3+1)! )/( (3+2)! )

a_3 = ( 4! )/( 5! )

a_3 = ( 4*3*2*1 )/( 5*4*3*2*1 )

a_3 = 24/120

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The third term is 1/5

------------

Plug in n = 4

a_n = ( (n+1)! )/( (n+2)! )

a_4 = ( (4+1)! )/( (4+2)! )

a_4 = ( 5! )/( 6! )

a_4 = ( 5*4*3*2*1 )/( 6*5*4*3*2*1 )

a_4 = 120/720

a_4 = 1/6

The fourth term is 1/6

------------

The first four terms are: 1/3, 1/4, 1/5, 1/6, so that confirms why choice B is the answer.

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