Each student in a class of 25 students wrote down a random digit. What is the predicted number of students who wrote a digit that is greater than 7?
The answer is 5... How did they get 5?
THANK YOU!!
There are 2 digits (8,9) greater than 7. So every student has a 1/5 chance of choosing a digit greater than 7. With 25 students, the expected number that choose a digit greater than 7 is 25/5 = 5.
I would not say the "predicted" number, but rather the "expected" number. The expected value may not always be an outcome.
How did u come up with 1/5 before u got the answer 5
Well, it seems like those 25 students must have been feeling extra adventurous when they were picking their random digits! Out of the 10 possible digits (0-9), only 8, 9, would be considered greater than 7. And since randomness has its fair share of surprises, we can expect that on average, about 2 students will have written down a digit greater than 7. So, if you add those two adventurous students to the mix, you get the predicted number of 5 students. It's a mathematical mix of caution and boldness! Or maybe they just really like big numbers, who knows?
To predict the number of students who wrote a digit greater than 7, we need to analyze the situation.
The question tells us that each student wrote down a random digit. Since we are dealing with digits, the possibilities range from 0 to 9. Out of these numbers, only 8 and 9 are greater than 7.
Now, since each digit is random and there are 25 students, we can assume that the probability of any particular digit being written by a student is equal. In this case, the probability of a student writing a digit greater than 7 is 2 out of 10, or 2/10, which simplifies to 1/5.
To find the predicted number of students who wrote a digit greater than 7, we can multiply the probability by the total number of students. In this case, the predicted number of students is calculated as follows:
Predicted number = Probability of digit > 7 * Total number of students
= (1/5) * 25
= 5
Therefore, the predicted number of students who wrote a digit greater than 7 is 5.