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Chapter 4: Problem 24

Clarkson University surveyed alumni to learn more about what they think of Clarkson. One part of the survey asked respondents to indicate whether their overall experience at Clarkson fell short of expectations, met expectations, or surpassed expectations. The results showed that \(4 \%\) of the respondents did not provide a response, \(26 \%\) said that their experience fell short of expectations, and \(65 \%\) of the respondents said that their experience met expectations (Clarkson Magazine, Summer 2001). a. If we chose an alumnus at random, what is the probability that the alumnus would say their experience surpassed expectations? b. If we chose an alumnus at random, what is the probability that the alumnus would say their experience met or surpassed expectations?

Short Answer

Expert verified
a. 5%; b. 70%.

Step by step solution

01

Understanding the Given Data

The problem provides the following data about an alumni survey: 4% did not respond, 26% said their experience fell short, and 65% said their experience met expectations. We need to use this data to solve the given probability questions.
02

Calculating Probability for Surpassed Expectations

We want to find the probability that an alumnus says their experience surpassed expectations. Knowing that 4% didn't respond, 26% fell short, and 65% met expectations, we can conclude that: - 100% of respondents minus 4% (no response) minus 26% (fell short) minus 65% (met) equals the percentage who said it surpassed expectations. - Thus, 100% - 4% - 26% - 65% = 5%. Therefore, the probability that an alumnus says their experience surpassed expectations is 5%.
03

Calculating Probability for Met or Surpassed Expectations

We need to calculate the probability that an alumnus said their experience either met or surpassed expectations. From the data, 65% met expectations and 5% surpassed expectations. Therefore, the sum of these two probabilities gives us the total probability for 'met or surpassed'. - Add 65% (met) + 5% (surpassed) = 70%. Thus, the probability that an alumnus said their experience met or surpassed expectations is 70%.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Understanding Statistics in Probability
Statistics is a branch of mathematics dealing with data collection, analysis, interpretation, and presentation. It plays a crucial role in survey data analysis, helping us make sense of the raw data collected from respondents. This exercise is a classic example of using statistical methods to determine probabilities from survey responses.

When Clarkson University conducted their alumni survey, they generated data that could be analyzed statistically to determine probabilities. The data given tells us how many alumni fell into each of the response categories. To find the probability of a specific response, we divide the number of respondents who gave that response by the total number of respondents.

In this case, to find the probability of an alumnus who said their experience surpassed or met expectations, we calculated it by adding their separate probabilities, derived from their percentage values. Recognizing these probabilities helps in understanding what general perceptions are prevalent among the alumni.
Survey Data Analysis Techniques
Survey data analysis refers to the process of organizing and interpreting data collected from surveys. This can include calculating percentages, identifying trends, and drawing conclusions from the survey responses. The Clarkson University survey data serves as an example.

In the survey, alumni feedback was categorized into non-response, fell short, met, and surpassed expectations. Each percentage directly translates to how the alumni felt about their experience at the university. Calculations for missing categories, such as surpassed expectations, were derived by subtracting the given percentages from 100% 鈥� since all possible responses must collectively add up to the total of 100%.

Survey data like this is analyzed using statistical methods to infer patterns. For example, by understanding whether more alumni met or exceeded their expectations, the university can gauge overall satisfaction. This insight can subsequently inform strategic decisions and improvements.
Interpreting Data for Insights
Data interpretation involves analyzing and applying the conclusions drawn from data鈥攁 crucial step after survey data analysis. In our example, observing that 70% of the respondents were either satisfied or exceeded their expectations gives Clarkson University valuable insights.

This analysis also involves understanding the significance of the numbers. For instance, only a small percentage (5%) of alumni report experiences that surpassed expectations. Depending on the university's goals, this could indicate room for improvement. Meanwhile, the 26% who felt that their experience fell short suggests areas that may need attention.

Interpreting these data points allows the institution to identify strengths and weaknesses in their alumni experiences. It's about turning raw percentage data into knowledge that can inform better decision-making, whether that means bolstering communication, changing policy, or other improvements to enhance the student and alumni experience.

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Most popular questions from this chapter

High school seniors with strong academic records apply to the nation's most selective colleges in greater numbers each year. Because the number of slots remains relatively stable, some colleges reject more early applicants. The University of Pennsylvania received 2851 applications for early admission. Of this group, it admitted 1033 students early, rejected 854 outright, and deferred 964 to the regular admissions pool for further consideration. In the past, Penn has admitted about \(18 \%\) of the deferred early admission applicants during the regular admission process. Counting the additional students who were admitted during the regular admission process, the total class size was 2375 (USA Today, January 24,2001 ). Let \(E, R,\) and \(D\) represent the events that a student who applies for early admission is admitted early, rejected outright, or deferred to the regular admissions pool. a. Use the data to estimate \(P(E), P(R),\) and \(P(D)\) b. Are events \(E\) and \(D\) mutually exclusive? Find \(P(E \cap D)\) c. For the 2375 students admitted to Penn, what is the probability that a randomly selected student was accepted for early admission? d. Suppose a student applies to Penn for early admission. What is the probability the student will be admitted for early admission or be deferred and later admitted during the regular admission process?

Suppose that we have a sample space with five equally likely experimental outcomes: \(E_{1}\) \(E_{2}, E_{3}, E_{4}, E_{5} \text { . Let } \) \\[ \begin{aligned} \qquad \begin{aligned} A &=\left\\{E_{1}, E_{2}\right\\} \\ B &=\left\\{E_{3}, E_{4}\right\\} \\ C &=\left\\{E_{2}, E_{3}, E_{5}\right\\} \end{aligned} \end{aligned} \\] a. Find \(P(A), P(B),\) and \(P(C)\) b. Find \(P(A \cup B)\). Are \(A\) and \(B\) mutually exclusive? c. \(\quad\) Find \(A^{c}, C^{c}, P\left(A^{c}\right),\) and \(P\left(C^{c}\right)\) d. Find \(A \cup B^{c}\) and \(P\left(A \cup B^{c}\right)\) e. Find \(P(B \cup C)\)

A consulting firm submitted a bid for a large research project. The firm's management initially felt they had a \(50-50\) chance of getting the project. However, the agency to which the bid was submitted subsequently requested additional information on the bid. Past experience indicates that for \(75 \%\) of the successful bids and \(40 \%\) of the unsuccessful bids the agency requested additional information. a. What is the prior probability of the bid being successful (that is, prior to the request for additional information)? b. What is the conditional probability of a request for additional information given that the bid will ultimately be successful? c. Compute the posterior probability that the bid will be successful given a request for additional information.

A company that manufactures toothpaste is studying five different package designs. Assuming that one design is just as likely to be selected by a consumer as any other design, what selection probability would you assign to each of the package designs? In an actual experiment, 100 consumers were asked to pick the design they preferred. The following data were obtained. Do the data confirm the belief that one design is just as likely to be selected as another? Explain. $$\begin{array}{cc} \text { Design } & \text { Number of Times Preferred} \\ 1 & 5 \\ 2 & 15 \\ 3 & 30 \\ 4 & 40 \\ 5 & 10 \end{array}$$

A telephone survey to determine viewer response to a new television show obtained the following data. $$\begin{array}{lc} \text { Rating } & \text { Frequency } \\ \text { Poor } & 4 \\ \text { Below average } & 8 \\ \text { Average } & 11 \\ \text { Above average } & 14 \\ \text { Excellent } & 13 \end{array}$$ a. What is the probability that a randomly selected viewer will rate the new show as average or better? b. What is the probability that a randomly selected viewer will rate the new show below average or worse?
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