# Discrete or Continuous? II Identify the following as discrete or continuous random variables: a.Number of overdue accounts in a department store at a particular time b.Your blood pressure

Question
Random variables
Discrete or Continuous? II Identify the following as discrete or continuous random variables:
a.Number of overdue accounts in a department store at a particular time

2021-02-20
(a)Given:
Numberof overdue accounts in a department store at a particular time.
Calculation:
Number of overdue accounts in a department store at a particular time is a discrete random variable that can take value from {0,1,2...}.
(b)Given:
Calculation:
My blood pressure is a continuous random variable.

### Relevant Questions

Discrete or Continuous? Identify the following as discrete or continuous random variables:
a. Total number of points scored in a football game
b. Shelf life of a particular drug
c. Height of the ocean's tide at a given location
d. Length of a 2-year-old black bass
e. Number of aircraft near-collisions in a year
Discrete or Continuous? II Identify the following as discrete or continuous random variables:
a. Increase in length of life attained by a cancer patient as a result of surgery
b. Tensile breaking strength (in pounds per square inch) of 1-inch-diameter steel cable
c. Number of deer killed per year in a state wildlife preserve
Indicate whether the following variables are categorical or numerical? If they are numerical, state whether they are discrete or continuous.
(a) The price of randomly selected sweaters in a department store.
(b) The first three digits of the social security number of randomly selected US residents. The eye color of randomly selected Columbia students.
(c) The number of views of randomly selected YouTube videos. The speed of randomly selected cars on Broadway.
In each of the following, identify the variables are categorical nominal, or categorical ordinal, or numerical discrete or numerical continuous.
2.Pant size of a randomly selected male as S, M, L, XL, XXL.
The owner of a large equipment rental company wants to make a rather quick estimate of the average number of days a piece of ditch-digging equipment is rented out per person per time. The company has records of all rentals, but the amount of time required to conduct an audit of all accounts would be prohibitive. The owner decides to take a random sample of rental invoices. Fourteen different rentals of ditch-diggers are selected randomly from the files, yielding the following data. She wants to use these data to construct a $$99\%$$ confidence interval to estimate the average number of days that a ditch-digger is rented and assumes that the number of days per rental is normally distributed in the population. Use only the appropriate formula and/or statistical table in your textbook to answer this question. Report your answer to 2 decimal places, using conventional rounding rules.
DATA: 3 1 3 2 5 1 2 1 4 2 1 3 1 1
The table below shows the number of people for three different race groups who were shot by police that were either armed or unarmed. These values are very close to the exact numbers. They have been changed slightly for each student to get a unique problem.
Suspect was Armed:
Black - 543
White - 1176
Hispanic - 378
Total - 2097
Suspect was unarmed:
Black - 60
White - 67
Hispanic - 38
Total - 165
Total:
Black - 603
White - 1243
Hispanic - 416
Total - 2262
Give your answer as a decimal to at least three decimal places.
a) What percent are Black?
b) What percent are Unarmed?
c) In order for two variables to be Independent of each other, the P $$(A and B) = P(A) \cdot P(B) P(A and B) = P(A) \cdot P(B).$$
This just means that the percentage of times that both things happen equals the individual percentages multiplied together (Only if they are Independent of each other).
Therefore, if a person's race is independent of whether they were killed being unarmed then the percentage of black people that are killed while being unarmed should equal the percentage of blacks times the percentage of Unarmed. Let's check this. Multiply your answer to part a (percentage of blacks) by your answer to part b (percentage of unarmed).
Remember, the previous answer is only correct if the variables are Independent.
d) Now let's get the real percent that are Black and Unarmed by using the table?
If answer c is "significantly different" than answer d, then that means that there could be a different percentage of unarmed people being shot based on race. We will check this out later in the course.
Let's compare the percentage of unarmed shot for each race.
e) What percent are White and Unarmed?
f) What percent are Hispanic and Unarmed?
If you compare answers d, e and f it shows the highest percentage of unarmed people being shot is most likely white.
Why is that?
This is because there are more white people in the United States than any other race and therefore there are likely to be more white people in the table. Since there are more white people in the table, there most likely would be more white and unarmed people shot by police than any other race. This pulls the percentage of white and unarmed up. In addition, there most likely would be more white and armed shot by police. All the percentages for white people would be higher, because there are more white people. For example, the table contains very few Hispanic people, and the percentage of people in the table that were Hispanic and unarmed is the lowest percentage.
Think of it this way. If you went to a college that was 90% female and 10% male, then females would most likely have the highest percentage of A grades. They would also most likely have the highest percentage of B, C, D and F grades
The correct way to compare is "conditional probability". Conditional probability is getting the probability of something happening, given we are dealing with just the people in a particular group.
g) What percent of blacks shot and killed by police were unarmed?
h) What percent of whites shot and killed by police were unarmed?
i) What percent of Hispanics shot and killed by police were unarmed?
You can see by the answers to part g and h, that the percentage of blacks that were unarmed and killed by police is approximately twice that of whites that were unarmed and killed by police.
j) Why do you believe this is happening?
Do a search on the internet for reasons why blacks are more likely to be killed by police. Read a few articles on the topic. Write your response using the articles as references. Give the websites used in your response. Your answer should be several sentences long with at least one website listed. This part of this problem will be graded after the due date.
Loretta, who turns eighty this year, has just learned about blood pressure problems in the elderly and is interested in how her blood pressure compares to those of her peers. Specifically, she is interested in her systolic blood pressure, which can be problematic among the elderly. She has uncovered an article in a scientific journal that reports that the mean systolic blood pressure measurement for women over seventy-five is 133.0 mmHg, with a standard deviation of 5.1 mmHg.
Assume that the article reported correct information. Complete the following statements about the distribution of systolic blood pressure measurements for women over seventy-five.
a) According to Chebyshev's theorem, at least $$?36\% 56\% 75\% 84\%\ or\ 89\%$$ of the measurements lie between 122.8 mmHg and 143.2 mmHg.
b) According to Chebyshev's theorem, at least $$8/9 (about\ 89\%)$$ of the measurements lie between mmHg and mmHg. (Round your answer to 1 decimal place.)
In each of the following, identify the variables are categorical nominal, or categorical ordinal, or numerical discrete or numerical continuous.
1.Political affiliation of a voter
The manager at Publix recently received information that customer satisfaction dropped at noon due to overcrowding in the checkout aisle. As a result, the manager went to the main floor to record the number of customers waiting in aisles 1-10 at noon.
Which of the following choices would be an accurate description of the way the "number of customers" is used in this data set?
a. individuals for the data set
b. continuous qualitative variable for this data set
c. discrete qualitative variable for this data set
d. qualitative variable for this set
e. continuous quantitative variable for this data set
f. discrete quantitative variable for this data set
If $$X_{1},X_{2},...,X_{n}$$ are random variables, then
$$E(X_{1},+X_{2}+,...+X_{n})=E(X_{1})+E(X_{2})+...+ E(X_{n})$$ (2)