Question
2.33 College smokers: At a university,
a) Calculate the expected number of smokers in a random sample of 160 students from this university
(please do not round your answer):
a) Calculate the expected number of smokers in a random sample of 160 students from this university
(please do not round your answer):
Ask by Gibbs Lambert. in the United States
Dec 07,2024
Upstudy AI Solution
Tutor-Verified Answer
Answer
The expected number of smokers in a sample of 160 students is
Solution
To calculate the expected number of smokers in a random sample of 160 students from the university, we can use the formula for the expected value in a binomial distribution:
where:
-
is the expected number of smokers, -
is the total number of students in the sample, -
is the probability that a student smokes.
Given:
-
-
(which is 11% expressed as a decimal)
Now, we can substitute the values into the formula:
Calculating this gives:
Thus, the expected number of smokers in a random sample of 160 students from this university is
Answered by UpStudy AI and reviewed by a Professional Tutor
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Simplify this solution The Deep Dive
To find the expected number of smokers in a random sample of 160 students, you multiply the total number of students by the percentage of smokers. The calculation is as follows:
Expected number of smokers = Total students × Percentage of smokers
Expected number of smokers = 160 × 0.11 = 17.6
Expected number of smokers = 160 × 0.11 = 17.6
So, in a random sample of 160 students from the university, we expect approximately 17.6 smokers.
Now, let’s add some context.
At many universities, smoking behaviors can stem from various social factors, including peer pressure or stress-related habits. Understanding the smoking rate in a student population can prompt initiatives aimed at promoting healthier alternatives, fostering a better campus environment.
When working with probabilities and expected values, it’s essential to remember that the calculated expected value may not necessarily be a whole number. In practice, since you can’t have a fraction of a person, this means that in any particular sample you would find either 17 or 18 smokers, showcasing the variability in real-world situations!
