A certain state has the highest high school graduation rate of all states at85​%. a. In a random sample of20high school students from the​ state, what is the probability that16will​ graduate?b. In a random sample of20high school students from the​ state, what is the probability than15or fewer will​ graduate?c. What is the probability that at least16high school students in our sample of20will​ graduate?  Please be very specific every question I have asked has been incorrect so far.

Question
Asked Oct 26, 2019
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A certain state has the highest high school graduation rate of all states at
85​%.
 
a. In a random sample of
20
high school students from the​ state, what is the probability that
16
will​ graduate?
b. In a random sample of
20
high school students from the​ state, what is the probability than
15
or fewer will​ graduate?
c. What is the probability that at least
16
high school students in our sample of
20
will​ graduate?
 
 
Please be very specific every question I have asked has been incorrect so far. 
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Expert Answer

Step 1

Solution: We are given that a certain state has the highest high school graduation rate of all states at 85​%

Let x be the number of high school graduates. Then the random variable x follows binomial distribution with p = 0.85, n = 20

and below probability mass function:

 

п!
Р(X — х).
P'(1-р)"
(п-х)!xPU- р)*
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Image Transcriptionclose

п! Р(X — х). P'(1-р)" (п-х)!xPU- р)*

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Step 2

a. In a random sample of 20 high school students from the​ state, what is the probability that 16 will​ graduate?

Answer: Here we have to find:

 

20!
Р(X %3 16) —
0.85"(1-0.85
(20-1616!
-0.1821
The excel function to find this answer is:
BINOMDIST(6,20,0.85, FALSE)
16 is x,
20 is n and 0.85 is p and False means we have to
find the probability of single outcome
help_outline

Image Transcriptionclose

20! Р(X %3 16) — 0.85"(1-0.85 (20-1616! -0.1821 The excel function to find this answer is: BINOMDIST(6,20,0.85, FALSE) 16 is x, 20 is n and 0.85 is p and False means we have to find the probability of single outcome

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Step 3

b. In a random sample of 20 high school students from the​ state, what is the probability ...

P 15) 1-P(216)
-1-(P(r-16)P(x-17)+Pr18) Px-19)Px20)
-1-(0.18212 +0.24283 +0.22934+0.13680 +0.03876)
-1-0.82985 0.1702
The excel finction to find this arswer is:
BINOMDIST(5,20,0.85,TRUE)
15 is x, 20 isn and 0.85 is p and TRUE means we have to
find the cumalative probability distribtion
help_outline

Image Transcriptionclose

P 15) 1-P(216) -1-(P(r-16)P(x-17)+Pr18) Px-19)Px20) -1-(0.18212 +0.24283 +0.22934+0.13680 +0.03876) -1-0.82985 0.1702 The excel finction to find this arswer is: BINOMDIST(5,20,0.85,TRUE) 15 is x, 20 isn and 0.85 is p and TRUE means we have to find the cumalative probability distribtion

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