In which of the following cases can the Normal Distribution be employed to estim
ID: 3334628 • Letter: I
Question
In which of the following cases can the Normal Distribution be employed to estimate the probabilities? If it cannot be used, why not?
1) A fair coin is tossed 9 times. Find the probability that the number of tails is less than 5.
2) A fair coin is tossed 11 times. Find the probability that the number of tails is less than 5.
3) A die is rolled 36 times. Find the probability that the sum of the numbers that face up is greater than 17.
4) Clinical trial on a new drug is done on a 100 patients. Estimate the probability that on average the drug is more effective than a placebo.
5) Ask 50 students on campus if they text while driving. Estimate the probability that the number of students who text while driving is greater than a 4000.
Explanation / Answer
1) A fair coin is tossed 9 times. Find the probability that the number of tails is less than 5.
Since the toss of the coin has only two outcomes - heads and tails, binomial distribution can be applied.
2) A fair coin is tossed 11 times. Find the probability that the number of tails is less than 5.
Since the toss of the coin has only two outcomes - heads and tails, binomial distribution can be applied.
3) A die is rolled 36 times. Find the probability that the sum of the numbers that face up is greater than 17.
Since the roll of the dice has only six outcomes - 1,2,3,4,5,6, binomial distribution cannot be applied.
4) Clinical trial on a new drug is done on a 100 patients. Estimate the probability that on average the drug is more effective than a placebo.
Since there can be two possibilities - more effective or not, binomial distribution can be applied.
5) Ask 50 students on campus if they text while driving. Estimate the probability that the number of students who text while driving is greater than a 4000
Since there can be two replies - yes or no, binomial distribution can be applied.