Question

According to the US Bureau of Labor Statistics, in the United States, the employment rate measures the number of people who have a job as a percentage of the working age population. In January 2020 the rate was 61.2%.

A) Recognizing that this is a binomial situation, give the meaning S and F in this context. That is, define what you will classify as a "success" S and what you will classify as a "failure" F as it refers to being employed.

B) Next, give the values of n, p, and q.

C) Construct the complete binomial probability distribution for this situation in a table.

D) Using your table, find the probability that exactly six working aged persons are employed.

E) Find the probability that at least 5 working aged persons are employed.

F) Find the probability that fewer than 6 working aged persons are employed.

G) Find the mean and standard deviation of this binomial probability distribution.

H) By writing a sentence, interpret the meaning of the mean value found in (G) as tied to the context of the percentage of working aged persons in the US.

I) Is it unusual to have 8 working aged persons in a group of 10 who are employed? Briefly explain your answer.

Answer 1

Answer:

Given that:

According to the US Bureau of Labor Statistics, in the United States, the employment rate measures the number of people who have a job as a percentage of the working age population.

a) Recognizing that this is a binomial situation, give the meaning S and F in this context. That is, define what you will classify as a "success" S and what you will classify as a "failure" F as it refers to being employed.

while "failure"is the working age person not being employed .

b)  Next, give the values of n, p, and q.

Here , n=10,

p= 0.612 &

9 = 1-0.612= 0.388

c) Construct the complete binomial probability distribution for this situation in a table.

Let "x" be the number of working aged person who are employed .

we used Excel function to find Binomial probabilities .

X=x	P(X=x)	Excel function :
0	0.000077	=Binomial.dist(0,10,0.612,0)
1	0.0012	=Binomial.dist(1,10,0.612,0)
2	0.0087	=Binomial.dist(2,10,0.612,0)
3	0.0364	=Binomial.dist(3,10,0.612,0)
4	0.1005	=Binomial.dist(4,10,0.612,0)
5	0.1902	=Binomial.dist(5,10,0.612,0)
6	0..2501	=Binomial.dist(6,10,0.612,0)
7	0.2254	=Binomial.dist(7,10,0.612,0)
8	0.1333	=Binomial .dist(8,10,0.612,0)
9	0.0467	=Binomial .dist(9,10,0.612,0)
10	0.0074	=Binomial.dist (10,10,0.612,0)

d) Using your table, find the probability that exactly six working aged persons are employed.

P(x=6)=0.2501

e)Find the probability that at least 5 working aged persons are employed

f) Find the probability that fewer than 6 working aged persons are employed.

g) Find the mean and standard deviation of this binomial probability distribution.

The mean of X is

standard deviation

h) By writing a sentence, interpret the meaning of the mean value found in (G) as tied to the context of the percentage of working aged persons in the US.

The mean indicates that on an average 6.12 6 working aged persons are employed for a random sample of n=10

i) Is it unusual to have 8 working aged persons in a group of 10 who are employed? Briefly explain your answer.

P(x=8) =0.1333

Since the probability is greater than 0.05, it is not unusual to have 8 working aged persons in a group of 10 who are employed. That is, the probability of X=8 is not very small.

Therefore it is not unusual.