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.

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.

A popular U.S. automobile manufacturer has​ 10,000 dealerships located throughout the country. The automobile manufacturer has multiple brands within its​portfolio: a value brand that caters to younger​ clientele, a moderate brand that caters to middle class customers and​ finally, a premium brand which is marketed to wealthy clientele. The​ company's leadership, located at corporate​ headquarters, is very interested in the relationship between the median salary of potential customers and the​ company's revenue.​ Specifically, the company is concerned that if potential​ customers' salaries continue to not increase in the​ future, the​company's revenue will remain​ stagnant, which will in turn steer away potential investors and shareholders. The​ company's research department recently collected data for analysis in order to support​ leadership's upcoming discussion with shareholders and investors about the​ company's future revenue forecast. Sales figures from a random sample of 1000 dealerships were collected. The research division also conducted statistical​ analysis, using data provided by the Bureau of Labor and​ Statistics, to calculate the median salary of people living in the vicinity of these​ 1,000 dealerships. The Dealership​ Number, State, Median​ Salary, Annual​Sales, Number of Vehicles​ Sold, Square Footage and Quality Award Winner data were collected for these 1000 dealerships.

We have an interest in finding out if the different dealerships sell different kinds of cars. Although our data set does not contain a lot of​ detail, one way to find such differences is by looking at the combination of Annual Sales and Number of Vehicles Sold for each dealership.

Find the median values of Annual Sales and Number of Vehicles Sold.

The median value for Annual Sales is ​$__ ,and the median value for Number of Vehicles Sold is ​$__.

Create two new indicator variables that indicate if a dealership has above median Annual Sales and above median Number of Vehicles Sold​ (so called​median-splits). In order to obtain the indicator variables with​ StatCrunch, use the following menu and option​ selections, where the expressions have the format​"Annual

​Sales">​xxx,

xxx being the calculated median value​ (same for Number of Vehicles​ Sold).

Data​ > Compute​ > Expression​ > Build Expression​ > Compute

Now create the contingency table of these two new indicator variables.

What values do you find on the diagonal of this contingency table​ (upper-left and​ lower-right cells)?

The value in the​ upper-left cell is__, and the value in the​ lower-right cell is __ .

What values do you find on the​ anti-diagonal of this contingency table​ (upper-right and​ lower-left cells)?

The value in the​ upper-right cell is __ , and the value in the​ lower-left cell is __ .

Based on this contingency​ table, what is the conditional probability of a dealership with above median Number of Vehicles Sold having above median Annual​Sales?

The conditional probability is__ .

Based on this contingency​ table, what is the conditional probability of a dealership with above median Number of Vehicles Sold having below median Annual​Sales?

The conditional probability is__.

How would you describe the events dealership having above median Number of Vehicles Sold and dealership having below median Annual​ Sales?

Independent

or

Disjoint

Make a scatterplot of Annual Sales against Number of Vehicles Sold. In order to obtain the scatterplot with​ StatCrunch, use the following menu and option selections.

Graph​ > Scatter Plot​ > Select X​ & Y variable​ > Compute

Describe the relationship between Annual Sales against Number of Vehicles Sold.

At the fencing center,60% of the fencers use foil as their main weapon. We randomly survey25 fencers at the fencing center, What is the probability that among the 25 surveyed, the number of fencers who use foil as their main weapon is

a). exactly 15

b.) at most 10

c.)more than 17

. A family has n number of kids. The possibility of 2ⁿ combinations by gender has equal probability. In A, show that “the family has kids of both genders”. In B, please show “the family has at most one girl”. Please show that this event is dependent for n=2, but independent for n=3

The Honolulu Advertiser stated that in Honolulu there was an average of 667 burglaries per 200,000 households in a given year. In the Kohola Drive neighborhood there are 319 homes. Let r be the number of homes that will be burglarized in a year. Use the formula for Poisson distribution. Compute the probability for . Round your answer to the nearest ten thousandth.

You take a quiz that consists of 5 multiple-choice questions. Each question has 5 possible answers, only one of which is correct. You will randomly guess the answer to each question. The random variable represents the number of correct answers. Construct the probability distribution for this random variable.

Three independently working elements have been installed to signal the accident, each of which is triggered in an emergency with a probability of 0.6. A discrete random amount is the number of elements that worked in an accident. Find: range of distribution, numerical characteristics,   F((x) Buildgraph F(x).

show your work.

Suppose the number of radios in a household has a binomial distribution with parameters ?=21 and ?=35%.

Find the probability of a household having:

(a) 7 or 17 radios
(b) 15 or fewer radios
(c) 13 or more radios
(d) fewer than 17 radios
(e) more than 15 radios