Question

Please help i need this done 100 points

PROJECT: PROBABILITY
Statisticians use their knowledge of probability and statistics to make predictions. Businesses often hire people who know how to use statistics to persuade others to buy their products. In this project, you will get a chance to experience how probability and statistics can be applied to a real-world situation.

OBJECTIVES
Collect and organize data.
Calculate probabilities based on data.
Use measures of central tendency to persuade.
Read the following summary of some concepts that were presented in this unit. After reading, follow the directions given to complete the project.

The probability of an event P(E) is equal to the number of ways the event can happen (M) over the total number of outcomes (N).

In other words, P(E) = M/N. This formula calculates unconditional probabilities. Unconditional probability is independent of any other event.

The chart below represents the high temperatures in Phoenix in June of 1999. Suppose we want to know the probability that an observation picked at random is a Thursday observation.



The above chart is understood as a universal set for June 1999, with a total count (N) of 30. Each day is a subset and has a count associated with it. The count for Thursdays is the characteristic of interest (M). We can see that this count is 5. The probability of any event P(E) = count of the characteristic of interest (M) divided by the count for the universal set (N). So, form a ratio between the number of Thursday observations and the total number of observations:

P(E) = M/N = 5/30 = 1/6 = 16.7%
Conditional Probability
In conditional probability, we are interested in probabilities under certain conditions. For example, what is the probability that an observation picked at random is on a Thursday when the temperature is between 90 and 99 degrees?

We are concerned only with temperature observations between 90 and 99 degrees. The chart shows the total count for this subset (N) is 6. The count for the characteristic of interest is the count of observations that occurred on a Thursday within the subset of observations that were between 90 and 99 degrees. Looking at the 90-99 row and the Thursday column, we see 2 hash marks (M). The conditional probability of the event P(E) = count of the characteristic of interest (M) divided by the count for the subset (N) being considered. So, form a ratio between the number of Thursday observations within the 90 to 99 degree range and the total number of observations in the 90 to 99 range:

P(E) = M/N = 2/6 = 1/3 = 33.3%
Joint Probability
Suppose we had two qualities, like day of the week and temperature, for which we wanted a probability. Let's find the probability that the day is Sunday (D) and the temperature (T) is less than 80. Look at the chart. For D, find Sunday, and for T, find temperatures less than 80. The chart tells us the number we want is 1, and the universal set is thirty, so the answer to the question is 1/30.

Your task:
Using your newspaper or another source, collect data on the high (or low) temperature and the day of the week for your city for one month. After gathering the data, complete the tasks listed below:

I. Construct a chart like the sample in the discussion. Try to have no fewer than five class intervals. "Class interval" refers to the number of categories a type of data could fall into (e.g., 70-79 degrees, 80-89 degrees, etc.).
II. Compute the probability that an observation picked at random will be a Saturday observation.

III. Repeat number two for the remaining days of the week.

IV. Use the chart in the discussion to answer these questions:

What is the probability a day in the 70s is a Monday?
Which set forms the intersection of Tuesdays in the 80s?
What is the probability an observation picked at random is both a Sunday and more than 90 degrees?
V. Construct a histogram to display the temperature frequencies for the month. (Use temperature class intervals and totals.)

VI. Pretend that you are working for the tourist bureau for your city. Which measure of central tendency (mean, median, mode) would you use in advertising to attract tourists. Justify your answer.

Complete tasks I-VI on your own paper. Upload your document to your teacher.

Answer 1

Here's a breakdown of the tasks:

I. Construct a chart: Collect data on the high (or low) temperature and the day of the week for your city for one month. Organize the data into a chart with columns for temperature intervals (class intervals) and rows for each day of the week. Count the number of observations that fall into each temperature interval for each day.

II. Compute the probability for Saturday: Determine the count for Saturday observations in your data and divide it by the total count of observations to calculate the probability of an observation being a Saturday.

III. Repeat for other days of the week: Compute the probability for each remaining day of the week using the same approach as in step II.

IV. Use the chart to answer questions: Refer to the chart and calculate the probabilities based on the provided information. For example:

- To find the probability of a day in the 70s being a Monday, locate the Monday row and the temperature interval corresponding to the 70s. Divide the count in that intersection by the total count of observations in the 70s.

- The intersection of Tuesdays in the 80s refers to the count of observations that are both on a Tuesday and fall into the 80s temperature interval.

- To find the probability of an observation being both a Sunday and more than 90 degrees, locate the Sunday row and the temperature interval greater than 90. Divide the count in that intersection by the total count of observations greater than 90.

V. Construct a histogram: Create a histogram to display the frequency of temperatures for the month. Group the temperatures into suitable class intervals on the x-axis and plot the frequency of each interval on the y-axis.

VI. Choose a measure of central tendency: Consider which measure of central tendency (mean, median, mode) would be most effective in advertising to attract tourists. Justify your choice based on the characteristics of your temperature data and the aspect of temperature that you want to emphasize to tourists. For example, if you want to highlight the typical or average temperature, the mean might be appropriate. If you want to emphasize the most frequently occurring temperature, the mode might be more suitable. Explain your reasoning.

Remember to document your work and calculations on your own paper and upload it to your teacher as instructed.

Answer 2

Here it is

Step-by-step explanation:

I hope this will help you and wish you a good score!!

(you know how much i struggled thru this just by looking at those scrumbs :))

+sorry for my bad handwritings xo