Consider the following binomial random variables.
(a) The number of tails seen in 58 tosses of a quarter.
(i) Find the mean. (Give your answer correct to one decimal place.)
0.3
Incorrect: Your answer is incorrect.
(ii) Find the standard deviation. (Give your answer correct to two decimal
places.)
To find the mean of a binomial random variable, we can use the formula:
Mean = n * p
where n is the number of trials (in this case, the number of tosses) and p is the probability of success (in this case, the probability of getting tails on a single toss).
(a) The number of tosses is 58 and the probability of getting tails on a single toss is 0.5 (assuming a fair quarter).
Mean = 58 * 0.5 = 29
So, the mean of the given binomial random variable is 29.
To find the standard deviation of a binomial random variable, we can use the formula:
Standard Deviation = sqrt(n * p * (1-p))
(b) Using the same values for n and p as before, we can calculate the standard deviation:
Standard Deviation = sqrt(58 * 0.5 * (1-0.5))
Standard Deviation = sqrt(58 * 0.5 * 0.5)
Standard Deviation = sqrt(14.5)
Standard Deviation ≈ 3.81
So, the standard deviation of the given binomial random variable is approximately 3.81, correct to two decimal places.