Exercise 3.29. In a school there are four kindergarten classes, with 21, 24, 17 and 28 students. We choose one of the 90 kindergarten students randomly, and denote the number of students in her class by X. Find the expectation and variance of X.

Expected mean = 23.2159

Variance = 15.89

Step-by-step explanation:

Given that :

Number of kindergarten students (X) :

21 + 24 + 17 + 28 = 90

P(X):

21/ 90 = 0.233

24/90 = 0.2667

17/90 = 0.1889

28/90 = 0.3111

X : 21 24 17 28

P(x) : _ 0.233 _ 0.2667 __ 0.1889 __ 0.3111

E(X) = Σ[(p)*p(x)]

(21 * 0.233) + (24 * 0.2667) + (17 * 0.1889) + (28 * 0.3111) = 23.2159

Var(X) : Σ(x²*p(x)) - E(x)²

x² * p(x) = (21^2 * 0.233) + (24^2 * 0.2667) + (17^2 * 0.1889) + (28^2 * 0.3111) - 23.2159^2

554.8667 - 538.97801281

= 15.88868719

= 15.89

2.2°  

step-by-step explanation:

let θ = the angle of elevation.

tanθ =77/2020

tanθ = 0.038 12

      θ = tan⁻¹0.038 12

      θ = 2.2°

answer 1 : option "c"

answer 2 : option "d"

answer 3 : option "b"

answer 4 : option "d"

answer 5 : option "b"

answer 6 : option "a"

answer 7 : option "c"

answer 8 : option "d"

answer 9 : option "c"

answer 10 : option "d"

answer 11 : option "c"

answer 12 option "b"

answer 13 option "c"

answer 14 option "c"

answer 15 option "d"

answer 16 option "a"

answer 17 option "b"

answer 18 option "c"

answer 19 option "a"

answer 20 option "a"

answer 21 option "c"

d