Question

The probability that a tennis set will go to a tiebreaker is 16%. In 220 randomly selected tennis sets, what is the mean and the standard deviation of the number of tiebreakers?

		mean: 35.2; standard deviation: 5.93
		mean: 33; standard deviation: 5.93
		mean: 35.2; standard deviation: 5.44
		mean: 33; standard deviation: 5.44

Answer 1

Solution:

Let X be the binomial random variable with the parameter n=220 and the probability, p=0.16.That means

??X?Bin(220,0.16)??

Then,

q=1-p = 1-0.16=0.84

Mean of the binomial distribution is = np = 2200.16=35.2

Hence,Mean=35.2

Then,The Standard deviation of the Binomial distribution given as:

Standard Deviation,???=? npq ??

???=? 220×0.16×0.84 ??

=??? 29.568 ?? =5.44

Hence, Standard deviation of the binomial random variable X is 5.44

Therefore, Mean=35.2 and Standard Deviation=5.44

Option (c) is correct.

Cheers!!