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The PTA at Bill Moore Junior High said that they will request the school information administration to change the school's mascot if at least 75 of 110 PTA members approve it. You interviewed a random sample of 32 members and found that 23 of them approve it. Based on your survey, do you think enough parents will approve the decision.


A=No, In the present survey sample, everyone did not approve it.

B=Cannot decide because the sample does not include all the parents

C=Yes, because everyone likes a change

D=Yes. Based on the sample, almost 80 parents will approve it.

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Answer:

D=Yes. Based on the sample, almost 80 parents will approve it.

Step-by-step explanation:

#We determine the proportion of approvals from the sample:

[tex]\hat p=\frac{x}{n}\\\\=\frac{23}{32}\\\\=0.71875[/tex]

#We then use this proportion to estimate the expected value of approvals in the population:

[tex]E(X)=n\hat p\\\\=110\times 0.71875\\\\\approx 80[/tex]

It is  likely that 80 people (5 more than the required number) will vote for the mascot change.

Hence, D is the correct option.

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