The Higher Education Research Institute at UCLA collected data from 302,458 incoming freshmen from 315 four-year college and universities in the Unitéd States. 74.5% of those students replied that, yes, they believe that same-sex couples should have the right to legal marital status. Suppose that you randomly pick eleven freshmen from the survey. You are interested in the number that believe that same-sex couples should have the right to legal marital status. Find the probability that exactly 4 of the 11 freshmen sampled believe that same-sex couples should have the right to legal marital status. Find the probability that at least'9 of the 11 freshmen sampled believe that same-sex couples should have the right to legal marital status. Find the mean of the distribution. Find the standard deviation of the distribution. Ouestion Holn ORest to forum

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
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Author:Carter
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Chapter10: Statistics
Section10.6: Summarizing Categorical Data
Problem 27PPS
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The Higher Education Research Institute at UCLA collected data from 302,458 incoming freshmen
from 315 four-year college and universities in the Unitéd States. 74.5% of those students replied
that, yes, they believe that same-sex couples should have the right to legal marital status. Suppose
that you randomly pick eleven freshmen from the survey. You are interested in the number that
believe that same-sex couples should have the right to legal marital status.
X ~ 7
Find the probability that exactly 4 of the 11 freshmen sampled believe that same-sex couples should
have the right to legal marital status.
Find the probability that at least 9 of the 11 freshmen sampled believe that same-sex couples
should have the right to legal marital status.
Find the mean of the distribution.
Find the standard deviation of the distribution.
Ouection Heln O Rect to foruum
Transcribed Image Text:The Higher Education Research Institute at UCLA collected data from 302,458 incoming freshmen from 315 four-year college and universities in the Unitéd States. 74.5% of those students replied that, yes, they believe that same-sex couples should have the right to legal marital status. Suppose that you randomly pick eleven freshmen from the survey. You are interested in the number that believe that same-sex couples should have the right to legal marital status. X ~ 7 Find the probability that exactly 4 of the 11 freshmen sampled believe that same-sex couples should have the right to legal marital status. Find the probability that at least 9 of the 11 freshmen sampled believe that same-sex couples should have the right to legal marital status. Find the mean of the distribution. Find the standard deviation of the distribution. Ouection Heln O Rect to foruum
Expert Solution
Step 1

As all incoming freshmen have only two options available whether to support same-sex marriage or oppose it. Hence, the opinion variable can be assumed to be following Binomial distribution.

Here, total independent trails(i.e participating freshmen) n=302458

Probability of success (i.e supporting same sex marriage) p=74.5%=0.745

As we have our parameters, i.e n and p,  then,

      X~B(n,p)X~B(302458,0.745)

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