Determine which if any of these experiments are binomial Tes

Determine which, if any, of these experiments are binomial. Testing a new pain reliever using 200 people to determine if it is effective. The random variable represents the number of people who find it effective. You roll a die 400 times. The random variable represents the number that roll. appears on each A only B only A&B; neither In a recent survey, 83% of the community\' favored building a police substation in their neighborhood. You randomly select 20 citizens and ask each if he or she thinks the community needs a police substation. Decide whether you can use the normal distribution to approximate the binomial distribution and if not, why not. You can use the normal distribution. You can\'t use the normal distribution because the sample is too small You can\'t use the normal distribution because 83% is too high a probability. You can\'t use the normal distribution because np(1-p} is not greater than 10.

Solution

12) For a binomial all events should be independent and prob for winning p means losing q i.e. there are only two outcomes.

A) For 200 people results for each is independent and outcomes is effective or not effective.

Hence binomial.

B) This is not binomial as X can take 1 to 6, 6 values.

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13) For approximating to normal distribution n should be large. Here n =20<30 minimum sample size for normal approximation.

Hence option b.