Answer:
0.172 ; 0.0884 ; 0.9115
Step-by-step explanation:
Proportion or those who feel secure, p = 0.45
Sample size, n = 8
Using the binomial distribution formula :
P(x =x) = nCx * p^x * (1 - p)^(n - x)
A.) p(x = 5)
P(x =5) = 8C5 * 0.45^5 * 0.55^3
P(x = 5) = 56 * 0.0184528125 * 0.166375
P(x = 5) = 0.1719248540625
P(x = 5) = 0.172
B.) P(x > 5)
P(x > 5) = P(x = 6) + P(x = 7) + P(x = 8)
P(x > 5) = 0.0703 + 0.0164 + 0.0017
P(x > 5) = 0.0884
C.) P( ≤ 5) = P(x = 0) + P(x = 1) + P(x = 2) + P(x = 3) + P(x = 4) + P(x = 5)
Using the binomial probability calculator to obtain a direct solution :
P( ≤ 5) = 0.9115
Answer: 86 or 60.
Step-by-step explanation:
Simplifying
2x + -3(3 * 0.6x + 2.7)
Multiply 3 * 0.6
2x + -3(1.8x + 2.7)
Reorder the terms:
2x + -3(2.7 + 1.8x)
2x + (2.7 * -3 + 1.8x * -3)
2x + (-8.1 + -5.4x)
Reorder the terms:
-8.1 + 2x + -5.4x
Combine like terms: 2x + -5.4x = -3.4x
-8.1 + -3.4x
Answer:
0.85083 ; 0.83147 ; 0.6823 ; 0.015386
Step-by-step explanation:
Given that:
σ = 25
μ = 86
(a) x is more than 60
P(x > 60)
obtain standardized score (Zscore)
Zscore = (x - μ) / σ
Z = (60 - 86) /25
Z = - 1.04
P(Z > - 1.04) = 0.85083 (Z probability calculator)
(b) x is less than 110
P(x < 110)
obtain standardized score (Zscore)
Zscore = (x - μ) / σ
Z = (110 - 86) /25
Z = 0.96
P(Z < 0.96) = 0.83147 (Z probability calculator)
(c) x is between 60 and 110
P(x < 110) - P(x < 60)
P(Z < 0.96) - P(Z < - 1.04)
0.83147 - 0.14917
= 0.6823
(d) x is greater than 140
P(x > 140)
obtain standardized score (Zscore)
Zscore = (x - μ) / σ
Z = (140 - 86) /25
Z = 2.16
P(Z > 2.16) = 0.015386 (Z probability calculator)
