Khaleesi Herbert

2021-02-25

A university found that of its students withdraw without completing the introductory statistics course. Assume that students registered for the course.
a. Compute the probability that or fewer will withdraw (to 4 decimals).
b. Compute the probability that exactly will withdraw (to 4 decimals).
c. Compute the probability that more than will withdraw (to 4 decimals).

pivonie8

Skilled2021-02-26Added 91 answers

The proportion is not mentioned, however "A university discovered that of its students withdraw without finishing the basic statistics course." Assume that p of the students drop out of the course before finishing. There are a total of students enrolled in the programme n$X\sim \text{Bin}(n,p)$Part (a): Calculate the likelihood that or fewer people will withdraw (to 4 decimals) Here, let's say that we need to determine the likelihood that fever or m will disappear. According to the definition of the mass function of X,$P(X=x)=\left(\begin{array}{}n\\ x\end{array}\right)\times {p}^{x}\times (1-p{)}^{n-x}$

$P(X\le m)=[P(X=0)+P(X=1)+...+P(X=m-1)]$Part (b): Determine the likelihood that a specific withdrawal will occur (to 4 decimals). The precise amount is not provided here either. Let's now presume that M will really withdraw. The likelihood that m' will withdraw precisely:$P(X={m}^{\prime})=\left(\begin{array}{c}n\\ {m}^{\prime}\end{array}\right)\times {p}^{x}\times (1-p{)}^{n-m}$Calculate the likelihood that more than M people will withdraw in part (c) (to 4 decimals). Assume that M is the necessary number. The likelihood that M or more people will withdraw:$P(X>M)=1-P(X\le M)$

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