Answer:
0.0918 ; 0.6277 ; 0.6064; 0.5055
Step-by-step explanation:
Given that :
Proportion of home owners : p = 0.52
Number of trials = 45
Using binomial distribution formula :
P(x =x) = nCr * p^x * (1 - p)^(n-x)
A.) probability that exactly 21 are homeowners :
P(x = 21) = 45C21 * 0.52^21 * (1 - 0.52)^(45 - 21)
P(x = 21) = 45C21 * 0.52^21 * 0.48^24
P(x = 21) = 3773655750150 * 0.52^21 * 0.48^24
P(x = 21) = 0.0918
b. At most 24 of them are are home
Using the binomial probability to save computation time.
P(x ≤ 24) = p(0) + p(1) +.... + p(24)
P(x ≤ 24) = 0.6277
C.) At least 23 of them are home owners.
P(x ≥ 23) = p(23) + p(24) +... + p(45)
P(x ≥ 23) = 0.6064
d. Between 20 and 24 (including 20 and 24) of them are home owners.
P(20 ≤ x ≤ 24) = p(20) + p(21) + p(22) + p(23) + p(24)
P(20 ≤ x ≤ 24) = 0.0711 + 0.0918 + 0.1084 + 0.1175 + 0.1167
P(20 ≤ x ≤ 24) = 0.5055
which is 16.2
which is 121