Which of the following variables have a binomial distribution? (I) You simultaneously flip a loonie with...

Which of the following variables have a binomial distribution?

(I)		You simultaneously flip a loonie with your left hand and a toonie with your right hand. You will do this ten times. X = number of times both coins land on Heads

(II)		GPAs at a large university follow a normal distribution with mean 3.00 and standard deviation 0.50. You take a random sample of 20 students. X = number of students in the sample with GPAs over 4.00

(III)		You record various weather statistics in Winnipeg every Saturday over the course of one year. X = number of Saturdays during the year that it snows in Winnipeg

Expert Solution

(I) Yes X = number of times both coins land on Heads will have Binomial distribution

Since, in each trail probability that coins land on Heads is constant and independent of the other trials

Also the number of trials is constant.

(II) Yes, X = number of students in the sample with GPAs over 4.00 follows Binomial distribution

As students GPA scores are independent, and probability that any one of the 20 students will score over 4 is constant.

The number of trials also finite, 20

(III) No, X = number of Saturdays during the year that it snows in Winnipeg

does not follow Binomial distribution as probability that on a Saturday it snows in Winnipeg can not independent.

orchestra answered 2 years ago

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