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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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).

2021-02-26
“A university found that of its students withdraw without completing the introductory statistics course” here percentage is not given. Let us assume that p of its student withdraw without completing in the course. The number of students registered for the course is n $$X \sim \text{Bin} (n, p)$$ Part (a): Compute the probability that or fewer will withdraw (to 4 decimals) Here let us assume that we have to find the probability that m or fever will withdraw. By the definition of mass function of X is given as: $$P(X=x)=\left(\begin{array}{a}n\\ x\end{array}\right) \times p^{x}\times (1-p)^{n-x}$$
$$P(X\leq m)=[P(X=0)+P(X=1)+...+P(X=m-1)]$$ Part (b): Compute the probability that exactly will withdraw (to 4 decimals). Here also the exact number is not given. Now assume that exactly m’ will withdraw. The probability that exactly m’ will withdraw: $$P(X=m')=\left(\begin{array}{c}n\\ m'\end{array}\right)\times p^{x}\times (1-p)^{n-m}$$ Part (c): Compute the probability that more than M will withdraw (to 4 decimals). Assume that the required number is M. The probability that more than M will withdraw: $$P (X > M) = 1 - P (X \leq M)$$

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