Answer:
Arithmetic sequence states that a sequence of numbers such that the difference between the consecutive terms is constant.
it is given by: where a is the first term , n is the number of term and d is the common difference.
Given the series:
here, Common difference(d) = 5
First term(a) = 49
by definition we have;
For nth term
= 5n + 44
To write the series using summation notation for 14 terms
Summation symbol
The series for 14th terms is given by;
Using the binomial distribution, the probabilities are given as follows:
a) 0.4159 = 41.59%.
b) 0.5610 = 56.10%.
c) 0.8549 = 85.49%.
<h3>What is the binomial distribution formula?</h3>The formula is:
The parameters are:
For this problem, the values of the parameters are:
n = 3, p = 0.76.
Item a:
The probability is P(X = 2), hence:
Item b:
The probability is P(X < 3), hence:
P(X < 3) = 1 - P(X = 3)
In which:
Then:
P(X < 3) = 1 - P(X = 3) = 1 - 0.4390 = 0.5610 = 56.10%.
Item c:
The probability is:
More can be learned about the binomial distribution at brainly.com/question/24863377
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