Question

The director of admissions at Kinzua University in Nova Scotia estimated the distribution of student admissions for the fall semester on the basis of past experience.
Admissions Probability 1,080 0.4 1,380 0.1 1,540 0.5

1. What is the expected number of admissions for the fall semester? Expected number of admissions 1340

2. Compute the variance and the standard deviation of the number of admissions. (Round your standard deviation to 2 decimal places.) Variance Standard deviation

Answer 1

Answer:

1. 1340

2. Variance = 47200, standard deviation = 217.25556

Step-by-step explanation:

1-

If X is the random variable that give the number of admissions, then the expected number of admissions E[X] for the fall semester is

1080*P(X=1080)+1380*P(X=1380)+1540*P(X=1540) =

1080*0.4+1380*0.1+1540*0.5 = 1340

2-

The variance is defined as

$\sigma^2=E[X^2]-(E[X])^2}$

We have

$E[X^2]=(1080)^2*0.4+(1380)^2*0.1+(1540)^2*0.5=1842800$

whereas

$(E[X])^2=(1340)^2=1795600$

So the variance equals

$\sigma^2=1842800-1795600=47200$

The standard deviation is just the square root of the variance, so, the standard deviation is

$\sigma=\sqrt{47200}=217.25556$