After years of teaching, I can say (with 100% made up certainty) that the average number of questions the typical student can complete per minute is 5. If I choose any student at random (I'm looking at you), what is the probability that yo...er that student could complete 7 questions in a minute?
The percentage is 10% toatl becuase you said 100% made up certantiy we cant solve this without your explantion Thanks and good luck
To find the probability that a student can complete 7 questions in a minute, we first need to understand the situation. The information given is that, on average, the typical student can complete 5 questions in a minute. However, it is not explicitly mentioned whether this distribution follows a particular pattern (such as normal distribution) or if it is uniformly distributed.
If we assume that the distribution follows a Poisson distribution with a mean of 5 (which is often used to model the number of events occurring in a fixed interval), we can calculate the probability of a student being able to answer 7 questions in a minute using the Poisson probability formula.
The Poisson probability formula is:
P(x; λ) = (e^(-λ) * λ^x) / x!
Where:
P(x; λ) is the probability of getting exactly x events (in this case, 7 questions) in a given interval,
e is Euler's number (approximately 2.71828),
λ (lambda) is the average number of events in the given interval (5 questions), and
x is the number of events (7 questions) we are interested in.
Let's plug in the values to calculate the probability:
P(7; 5) = (e^(-5) * 5^7) / 7!
To simplify the calculation further, we can use the approximation that e^(-5) is approximately 0.0067.
P(7; 5) ≈ 0.0067 * (5^7) / 7!
Now, let's calculate the numerator and denominator separately.
Numerator: 0.0067 * (5^7) ≈ 0.0067 * 78125 ≈ 523.4375
Denominator: 7! = 7 * 6 * 5 * 4 * 3 * 2 * 1 = 5,040
Finally, we can calculate the probability:
P(7; 5) ≈ 523.4375 / 5,040 ≈ 0.1036
Therefore, the probability that a randomly chosen student, based on the given information, can complete 7 questions in a minute is approximately 0.1036 or 10.36%.