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 of the respondents did not provide a response, said that their experience fell short of expectations, and of the respondents said that their experience met expectations. 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?

Question

Mathematics

Yang

18 June, 16:22

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 of the respondents did not provide a response, said that their experience fell short of expectations, and of the respondents said that their experience met expectations. 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?

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Answers (1)

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Trevin Hardy · Answer 1

Step-by-step explanation:

The question is incomplete. The complete question is:

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 respondents did not provide a response, 26% said that their experience fell short of expectations, 65% of the respondents said that their experience met expectations (Clarkson Magazine, Summer, 2001). If we chose an alumnus at random, what is the probability that the alumnus would say their experience surpassed expectations? If we chose an alumnus at random, what is the probability that the alumnus would say their experience met or surpassed expectations?

Solution:

Probability = number of favorable outcomes/number of total outcomes

From the information given,

The probability that respondents did not provide a response, P (A) is 4/100 = 0.04

The probability that a respondent said that their experience fell short of expectations, P (B) is 26/100 = 0.26

The probability that a respondent said that their experience met expectations, P (C) is 65/100 = 0.65

A) Adding all the probabilities, it becomes 0.04 + 0.26 + 0.65 = 0.95

Therefore, the probability, P (D) that a respondent said that their experience surpassed expectations is 1 - 0.95 = 0.05

B) The event of a randomly chosen respondent saying that their experience met expectations and that their experience surpassed expectations are mutually exclusive because they cannot occur together. It means that P (C) * P (D) = 0

Therefore, the probability of P (C) or P (D) is 0.65 + 0.05 = 0.7