Question

Given any undergraduate student, there is 10% chance that they will join the graduate program. In an undergraduate class of 400 students, which of the following is the closest to the probability that at least 50 students will be joining a graduate program?A. 5%B 10%c 15%D 20%E 25%

Answer 1

Answer: A. 5%

Step-by-step explanation:

Given : The chance that they will join the graduate program : p=0.10

The total number of students in the class: n = 400

For this binomial situation :

$\mu=np=400\times0.10=40\\\\\sigma=\sqrt{np(1-p)}=\sqrt{400\times0.10(0.90)}=6$

We assume that this is normal distribution.

Let X be the random variable that represents the students will be joining a graduate program.

Z-score : $z=\dfrac{x-\mu}{\sigma}$

For x= 50 , we have

$z=\dfrac{50-40}{6}=1.67$

Using the standard normal distribution table , we have

$P(x\geq50)=P(z\geq1.67)=1-P(z$

Hence, the value i.e.closest to the probability that at least 50 students will be joining a graduate program = 5%