In a recent poll, the Pew Research Center estimated that 47% of American adults who have used a dating site or app in the past year would say that it has been important to them that the profiles they look at include someone’s COVID-19 vaccination status.

2. [8 points] In a recent poll, the Pew Research Center estimated that 47% of American adults who have used 

a dating site or app in the past year would say that it has been important to them that the profiles they look at 

include someone’s COVID-19 vaccination status. Suppose that figure is correct.

We take a random sample of 240 American adults who have used a dating site or app in the past year. 

a. [1 point] What is the probability that exactly 120 of those adults in our sample would say that it has been 

important to them that the profiles they look at include someone’s COVID-19 vaccination status?

(Remember to explain how you got your answer!)

b. [1 point] What is the probability that more than 110 of the adults in our sample would say that it has been 

important to them that the profiles they look at include someone’s COVID-19 vaccination status? 

(Remember to explain how you got your answer!)

c. [1 point] What is the probability that at most 55% of the adults in our sample would say that it has been 

important to them that the profiles they look at include someone’s COVID-19 vaccination status?

(Remember to explain how you got your answer!)

d. [1 point] Consider the event “Less than half of the adults in our sample would say that it has been important 

to them that the profiles they look at include someone’s COVID-19 vaccination status.” Describe in words the 

complement of that event. Do not calculate a probability. 

e. [2 points] What is the expected value and the standard deviation of the number of people in our sample 

that would say that it has been important to them that the profiles they look at include someone’s COVID-19 

vaccination status? Round your answers to the nearest tenth, if necessary.

f. [2 points] If 100 people in the sample say that it has been important to them that the profiles they look at 

include someone’s COVID-19 vaccination status, would that be an unusually low number of people? Explain. 

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