Respuesta :
Answer:
a) P(X<20) ≅ 1
b) P(10<X<20) = 0.000495
c) P(X<20) ≅ 1
 P(10<X<20) = 0.000000838 ≅ 0
Step-by-step explanation:
Let be the event X : ''Number of adults having an income greater than $100,000''
We can modelate X as a Binomial random variable
X~Bi(n,x,p)
Where n is the number of the random sample
x is the X value (number of success)
p is the success probability
In our exercise :
[tex]n=25\\p=0.15[/tex]
The probability function of X is :
[tex]P(X=x)=f(x)=nCx.p^{x}.(1-p)^{n-x}[/tex]
Where [tex]nCx[/tex] is the combinatorial number : [tex]nCx=\frac{n!}{x!(n-x)!}[/tex]
For a)
[tex]P(X<20)=1-P(X\geq 20)=1-[f(20)+f(21)+f(22)+f(23)+f(24)+f(25)][/tex]
P(X<20) = 0.9999 ≅ 1
b)
[tex]P(10<X<20)=f(11)+f(12)+f(13)+f(14)+f(15)+f(16)+f(17)+f(18)+f(19)[/tex]
[tex]P(10<X<20)=0.000495[/tex]
c) Is the same as part a) but now the probability p =0.09
[tex]P(X<20) =1-P(X\geq 20)=1-[f(20)+f(21)+f(22)+f(23)+f(24)+f(25)][/tex]
P(X<20) =0.9999 ≅ 1
[tex]P(10<X<20)=f(11)+f(12)+f(13)+f(14)+f(15)+f(16)+f(17)+f(18)+f(19)[/tex]
P(10<X<20)=0.000000838≅0
The probabilities are given by binomial probability distribution are as follows;
a.  P(X < 20) ≅ 1
b. Â P(10 < X < 20) = 0.000495
c.  P(X < 20) ≅ 1 and P(10 < X < 20) = 0.000000838 ≅ 0
What is probability?
Probability means possibility. It deals with the occurrence of a random event. The value of probability can only be from 0 to 1. Its basic meaning is something is likely to happen. It is the ratio of the favorable event to the total number of events.
Playing sports related to job pay.
This was the subject of a recent Harris POLL (March 2015).
The poll found that 15% of adults who participated in sports now have an income greater than $100,000.
In comparison, 9% of adults who did not participate in sports have an income greater than $100,000.
Consider a random sample of 25 adults, all of whom have participated in youth and/or high school sports.
Let X be the number of adults having an income greater than $100,000.
We can modulate X as a Binomial distribution.
Let p be the probability of success and q be the probability of not succeeding.
n be the number of random samples.
x is a number of successes.
The probability function of X is given as
[tex]\rm P(X = x ) =f(x)= ^nC_x *p^x *q^{n-x}[/tex]
a. Â The probability of success less than 20 will be
[tex]\rm P(X < 20) = 1- P(X\geq 20) = 1- [f(20) + f(21) +f(22)+f(23)+f(24)+f(25)]\\\\P(X < 20) = 0.9999 \cong 1[/tex]
b. Â The probability of success is greater than 10 but less than 20 will be
[tex]\rm P(10 < X < 20) = f(11) + f(12) + f(13) + f(14) + f(15) + f(16) + f(17) + f(18) + f(19) \\\\P(10 < X < 20) = 0.000495[/tex]
c. Â Is the same as part a but now probability p = 0.09.
[tex]\rm P(X < 20) = 1- P(X\geq 20) = 1- [f(20) + f(21) +f(22)+f(23)+f(24)+f(25)]\\\\P(X < 20) = 0.9999 \cong 1[/tex]
[tex]\rm P(10 < X < 20) = f(11) + f(12) + f(13) + f(14) + f(15) + f(16) + f(17) + f(18) + f(19) \\\\P(10 < X < 20) = 0.000000838 \cong 0[/tex]
More about the probability link is given below.
https://brainly.com/question/795909
