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).

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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$X\sim \text{Bin}\left(n,p\right)$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,$P\left(X=x\right)=\left(\begin{array}{}n\\ x\end{array}\right)×{p}^{x}×\left(1-p{\right)}^{n-x}$
$P\left(X\le m\right)=\left[P\left(X=0\right)+P\left(X=1\right)+...+P\left(X=m-1\right)\right]$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:$P\left(X={m}^{\prime }\right)=\left(\begin{array}{c}n\\ {m}^{\prime }\end{array}\right)×{p}^{x}×\left(1-p{\right)}^{n-m}$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:$P\left(X>M\right)=1-P\left(X\le M\right)$

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