Respuesta :
Answer:
0.769296
Step-by-step explanation:
The desired probability can be calculated from binomial probability distribution because there are 21 independent trials and probability of success(saving nothing for retirement) 0.2 remains same for each trial. Here, n=21 and p=0.20. We want to compute P(X>5).
The pdf of binomial distribution is
P(X=x)=nCx(p)^x(1-p)^(n-x)
P(X>5)=1-P(X≤5)
P(X≤5)=P(X=0)+P(X=1)+P(X=2)+P(X=3)+P(X=4)+P(X=5)
P(X=0)=21C0*(0.2)^0*(1-0.2)^(21-0)=0.009223
P(X=1)=21C1*(0.2)^1*(1-0.2)^(21-1)=0.048423
P(X=2)=21C2*(0.2)^2*(1-0.2)^(21-2)=0.121057
P(X=3)=21C3*(0.2)^3*(1-0.2)^(21-3)=0.191673
P(X=4)=21C4*(0.2)^4*(1-0.2)^(21-4)=0.215632
P(X=5)=21C5*(0.2)^5*(1-0.2)^(21-5)=0.183287
P(X≤5)=0.009223+0.048423+0.121057+0.191673+0.215632+0.183287
P(X≤5)=0.769296
P(X≤5) can also be computed by using excel function BINOM.DIST(5,21,0.2,TRUE) which results in
P(X≤5)=0.769296.
The probability that more than five of the selected adults save nothing for retirement is; P(X > 5) = 0.239928
We are told that 20% of adults in the US save nothing for retirement. Thus;
p = 20% = 0.2
21 adults are selected randomly. Thus;
n = 21
Probability that more than five of the selected adults save for retirement is gotten from formula for binomial probability distribution which is;
P(X = x) = nCx × p^(x) × (1 - p)^(n - x)
Thus;
P(X > 5) = 1 - P(X ≤ 5)
Where;
P(X ≤ 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5)
P(X = 0) = 21C0 × 0.2^(0) × (1 - 0.2)^(21 - 0) =
0.009223
Using online binomial probability calculator, we can find the remaining as;
P(X = 1) = 0.048423
P(X = 2) = 0.121057
P(X = 3) = 0.191673
P(X = 4) = 0.215632
P(X = 5) = 0.183287
Thus;
P(X ≤ 5) = 0.048423 + 0.121057 + 0.191673 + 0.215632 + 0.183287
P(X ≤ 5) = 0.760072
Thus;
P(X > 5) = 1 - 0.760072
P(X > 5) = 0.239928
Read more about binomial probability distribution at; https://brainly.com/question/24239758
