Answer:
B. 279
Step-by-step explanation:
To estimate how many of the 360 people who saw the play would recommend it to their friends, we can use the ratio from the random sample.
Let x be the estimated number of people out of 360 who would recommend the play. Given that 31 people out of 40 in the sample said they would recommend the play, then:
[tex]\dfrac{x}{360}=\dfrac{31}{40}[/tex]
Multiply both sides by 360 and solve for x:
[tex]\dfrac{x}{360}\cdot 360=\dfrac{31}{40}\cdot 360\\\\\\\\x=\dfrac{11160}{40}\\\\\\\\x=279[/tex]
So, the best estimate is that approximately 279 out of the 360 people who saw the play would recommend it to their friends.
Answer:
279 people
Step-by-step explanation:
To estimate how many out of 360 people would recommend the play based on the responses from a random sample, we can use proportional reasoning based on the sample data.
Given:
We can set up a proportion to estimate the no. of people who would recommend the play out of the total 360 people.
The proportion is:
[tex]\boxed{\dfrac{\textsf{No. of recommenders in sample}}{\textsf{Total sample size}} = \dfrac{\textsf{No. of recommenders}}{\textsf{Total population size}}}[/tex]
Plugging in the values we have:
[tex]\dfrac{31}{40} = \dfrac{x}{360}[/tex]
To solve for [tex]\bold{x }[/tex](the estimated No. of recommenders among the 360 people who saw the play), cross-multiply and solve for [tex]\bold{x}[/tex]:
[tex]31 \times 360 = 40 \times x[/tex]
[tex]x = \dfrac{31 \times 360}{40}[/tex]
[tex]x = \dfrac{11160}{40}[/tex]
[tex]x = 279[/tex]
Therefore, the best estimate of how many out of the 360 people who saw the play would recommend it to their friends, based on the sample data, is [tex]\bold{ \boxed{279} }[/tex] people.
This estimate assumes that the proportion of recommenders within the sample (31 out of 40) is consistent with the proportion of recommenders in the total population of play attendees (out of 360 people).
