79% of the students at College University are about to finish their prerequisites. If 42 students are randomly selected find the probability that, Exactly 36 of them are done with their prerequisites At most 37 need two more classes At least 32 will finish next semester Between 30 to 38 (including 30 and 38) will finish by next year.
Contingency Table
A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.
Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
79% of the students at College University are about to finish their prerequisites. If 42 students are randomly selected find the
Exactly 36 of them are done with their prerequisites
At most 37 need two more classes
At least 32 will finish next semester
Between 30 to 38 (including 30 and 38) will finish by next year.
Given information
Probability that the student will finish the prerequisite p = 0.79
Number of students randomly selected = 42
Binomial theorem p.m.f
Probability of x success out of n trial is
b)
At most 37 need two more classes
P(X ≤ 37) = 0.7565(Using Excel =BINOM.DIST(37,45,0.79,TRUE) (Rounded upto 4 places of decimal)
c)
At least 32 will finish next semester
P(X≥32) = 1- P(X<32) = 1 – P(X ≤ 31) = 1 - 0.0736 = 0.9264(Rounded upto 4 places of decimal)
P(X ≤ 31) = 0.0736(Using Excel =BINOM.DIST(31,45,0.79,TRUE)
D)
Between 30 to 38 (including 30 and 38) will finish by next year.
P( 30 ≤ X ≤ 38) = P( X≤38) – P(X≤30) = 0.8618 – 0.0373 = 0.8245 (Rounded upto 4 places of decimal)
P(X ≤ 30) = 0.8618 (Using Excel =BINOM.DIST(30,45,0.79,TRUE)
P(X ≤ 38) = 0.0373 (Using Excel =BINOM.DIST(38,45,0.79,TRUE)
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