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. What is the expected number of admissions for the fall semester? Compute the variance and the standard deviation of the number of admissions.Admissions Probability1,000 .61,200 .31,500 .1

Answer 1

Answer:

Variance = 24900

Standard Deviation = 157.7973        

Step-by-step explanation:

We are given the following in the question:

Number of admissions:    1000     1200    1500

Admissions Probability:     0.6        0.3       0.1

Formula:

$E(x) = \displaystyle\sum x_iP(x_i)\\E(x) = 1000(0.6) + 1200(0.3) + 1500(0.1)\\E(x) = 1110\\E(x^2) = \displaystyle\sum x_i^2P(x_i)\\E(x^2) = (1000)^2(0.6) + (1200)^2(0.3) + (1500)^2(0.1)\\E(x^2) = 1257000$

Variance =

$\sigma^2 = E(x^2) - (E(x))^2\\\sigma^2 = 1257000 -(1110)^2\\\sigma^2 =24900$

Thus, the variance is 24900.

Standard Deviation =

$\sigma = \sqrt{\sigma^2} = \sqrt{24900} = 157.7973$

Thus, the standard deviation is 157.7973