Just need some help with this little condition(s)... Suppose 20% of students wat
ID: 2915847 • Letter: J
Question
Just need some help with this little condition(s)...Suppose 20% of students watch American Idol everyweek. Ten students are selected at random. Let X = the number ofstudents in the sample who watch American Idol everyweek.
Problem: The sample size is increased from 10 to 200. What isthe chance that AT LEAST 30% of the students watch American Idolevery week? (Check any conditions that must be met in order tosolve this problem).
I have an idea, but a little clarification please!Thanks.
Suppose 20% of students watch American Idol everyweek. Ten students are selected at random. Let X = the number ofstudents in the sample who watch American Idol everyweek.
Problem: The sample size is increased from 10 to 200. What isthe chance that AT LEAST 30% of the students watch American Idolevery week? (Check any conditions that must be met in order tosolve this problem).
I have an idea, but a little clarification please!Thanks.
Explanation / Answer
Since the sample size is decently large and p is not terribly closeto 0 or 1, we can solve this with a normal approximation of thebinomial distribution. Given the sample size n of 200 and p of 0.2,the normal distribution is N(np, np(1-p)) = N(40, 32). The probability that at least 30% of the students watch AmericanIdol is the probability that more than 60 students watch the showin a normal distribution with mean 40 and variance 32. Normalize the distribution to arrive at: Z = (60-40)/sqrt(32) = 3.53 The probability of being above 3.53 in a N(0,1) distribution isessentially 0.
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