Use inductive reasoning to determine the next two terms in each sequence: a) 1, 3, 7, 15, 31 ....
2 answers:
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Answer:
Step-by-step explanation:
Hello!
There are some values missing, so I'll find the probability distribution using others as example. Afterwards you can calculate the ones corresponding to this exercise following the same steps.
Considering there are 5000 undergraduates registered in the college.
465 are taking one course
658 are taking two courses
566 are taking three courses
1877 are taking four courses
1344 are taking five courses
90 are taking six courses
First you have to define the variable of interest. To identify it you have to ask yourself the following question: what is the characteristic of this population that is being measured?
The answer is "the number of courses an undergraduate is taking" and this will be the study variable X
X can take values from 1 to 6 courses.
To calculate the probability of each value of X, you have to divide the "number of students taking Xi courses" by "total number of students registered in the college"
For
X=1
P(1)= 465/5000= 0.093
X=2
P(2)= 658/5000= 0.1316
X=3
P(3)= 566/5000= 0.1132
X=4
P(4)= 1877/5000= 0.3754
X=5
P(5)= 1344/5000= 0.2688
X=6
P(6)= 90/5000= 0.018
For this to be a probability distribution the following condition should be met:
F(X)= ∑P(X) = 1
In this example: 0.093 + 0.1316 + 0.1132 + 0.3754 + 0.2688 + 0.018 = 1
I hope this helps!
