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Question

Étapes de solution

1. Understand the question

   since we are counting the number of children that have a food allergy, and we know about 20% of all children have a food allergy, the probability of success is $p = 0.20$.
   since there are 85 children in the sample, and each child is independent of others, we have $n = 85$ independent trials.
   the problem asks for the probability that exactly 15 of the 85 children have a food allergy.
   using the binomial distribution, we set the dot sliders to $p = 0.20$ and $n = 85$, and we set the dot slider on the $x$-axis to 15 to see the probability is 0.0969., which rounds to 0.097.
   feedback
   content attribution
   question
   assume that the probability above is 0.26. choose the best interpretation of this probability.
   select the correct answer below:
   a typical child has 26% of all food allergies.
   the probability that exactly 15 of the 85 children in the sample have a food allergy is 26%.
   26% of the 85 children in the sample have a food allergy.
   26% of all children have a food allergy.

2. Brief Explanations

   The probability value given refers specifically to the likelihood of the outcome (exactly 15 out of 85 children having a food allergy) occurring. The other options misinterpret the probability: the first confuses individual allergy share, the third states a observed proportion not a probability, and the fourth incorrectly restates the population allergy rate.

3. Final answer

   The probability that exactly 15 of the 85 children in the sample have a food allergy is 26%.

Réponse

Question Analysis

OCR Text

since we are counting the number of children that have a food allergy, and we know about 20% of all children have a food allergy, the probability of success is $p = 0.20$.
since there are 85 children in the sample, and each child is independent of others, we have $n = 85$ independent trials.
the problem asks for the probability that exactly 15 of the 85 children have a food allergy.
using the binomial distribution, we set the dot sliders to $p = 0.20$ and $n = 85$, and we set the dot slider on the $x$-axis to 15 to see the probability is 0.0969., which rounds to 0.097.
feedback
content attribution
question
assume that the probability above is 0.26. choose the best interpretation of this probability.
select the correct answer below:
a typical child has 26% of all food allergies.
the probability that exactly 15 of the 85 children in the sample have a food allergy is 26%.
26% of the 85 children in the sample have a food allergy.
26% of all children have a food allergy.

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