STATISTIKA DASAR NAMA : MENIK GUSTINASARI NIM : 642016006
SOAL 14
Penyelesaian Diketahui data berdistribusi normal dengan mean = 5ml dan standar deviasi σ = 0.2ml a. P(x < 5.0) = P(Z < ) = P(Z < ) = P(Z < 0) = 0.5000 b. P(x < 5.4) = P(Z < ) = P(Z < ) = P(Z < 2.0) = 0.9772
= 0.8351 c. P(x ≤ 5.4) = P(Z ≤ ) = P(Z ≤ ) = P(Z ≤ 2.0) = 0.9772 z1 = (x1 -μ)/σ z1 = (4.5-5)/0.2 = -2.5 z2 = (x2 -μ)/σ z2 = (5.2-5)/0.2 = 1.0 Sehingga P(4.5 < x < 5.2) = P(-2.5 < z < 1.0) P(-2.5 < z < 1.0) = P(z<1.0) – P(z<-2.5) = 0.8413 – 0.0062 = 0.8351
e. P(x > 4. 5) = P(Z > ) = P(Z > ) = P(Z > -2 e. P(x > 4.5) = P(Z > ) = P(Z > ) = P(Z > -2.5 ) = 1-P(Z < -2.5) = 1- 0.0062 = 0.9938 f. P(x > 4.0) = P(Z > ) = P(Z > -5.0 ) = 1-P(Z < -5.0) = 0.9999997