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:
[tex]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[/tex]
Variance =
[tex]\sigma^2 = E(x^2) - (E(x))^2\\\sigma^2 = 1257000 -(1110)^2\\\sigma^2 =24900[/tex]
Thus, the variance is 24900.
Standard Deviation =
[tex]\sigma = \sqrt{\sigma^2} = \sqrt{24900} = 157.7973[/tex]
Thus, the standard deviation is 157.7973
