Pregunta
A survey shows that about
college. Suppose that we randomly select 11 students from the college, please solve the following problems
and round your answers to 4 decimal places.
a. What is the probability that exactly 5 of them know HelpYourMath YouTube Channel?
a
b. What is the probability that at least 5 of them know HelpYourMath YouTube Channel?
c. What is the probability that at most 5 of them know HelpYourMath YouTube Channel?
d. What is the probability that more than 5 of them know HelpYourMath YouTube Channel?
e. What is the probability that less than 5 of them know HelpYourMath YouTube Channel?
college. Suppose that we randomly select 11 students from the college, please solve the following problems
and round your answers to 4 decimal places.
a. What is the probability that exactly 5 of them know HelpYourMath YouTube Channel?
a
b. What is the probability that at least 5 of them know HelpYourMath YouTube Channel?
c. What is the probability that at most 5 of them know HelpYourMath YouTube Channel?
d. What is the probability that more than 5 of them know HelpYourMath YouTube Channel?
e. What is the probability that less than 5 of them know HelpYourMath YouTube Channel?
Ask by Daniel Turner. in the United States
Mar 14,2025
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
Responder
a. 0.2335
b. 0.5725
c. 0.4275
d. 0.7665
e. 0.2335
b. 0.5725
c. 0.4275
d. 0.7665
e. 0.2335
Respondido por UpStudy AI y revisado por un tutor profesional
Como
Extra Insights
To solve these problems, we can use the binomial probability formula, which is:
Where:
-
= total number of trials (students selected) -
= number of successes (students that know the channel) -
= probability of success (students knowing the channel) -
= binomial coefficient
In this case,
a. Probability that exactly 5 know HelpYourMath YouTube Channel
Calculating the binomial coefficient and substituting the values:
So, the probability that exactly 5 students know the channel is approximately 0.1470.
b. Probability that at least 5 know HelpYourMath YouTube Channel
To find this, we calculate
Now we need to find
Calculating all of these probabilities and summing them will give the result.
Calculating:
So,
Thus, the probability that at least 5 students know the channel is approximately 0.3827.
c. Probability that at most 5 know HelpYourMath YouTube Channel
This is straightforward:
From the previous result:
Thus,
The probability that at most 5 students know the channel is approximately 0.7643.
d. Probability that more than 5 know HelpYourMath YouTube Channel
Using:
So, the probability that more than 5 students know the channel is approximately 0.2357.
e. Probability that less than 5 know HelpYourMath YouTube Channel
Using:
So, this is already calculated:
In conclusion:
- a.
- b.
- c.
- d.
- e. ( P(X < 5) \approx
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