Consider the binomial random variable x with n = 30 and p = 0.85.
(a) Find the mean. (Give your answer correct to one decimal place.)
25.5 .
(b) Find the standard deviation. (Give your answer correct to two decimal places.) 30.85
Mean is correct.
Standard deviation = sqrt(npq))
sqrt(30* .85 *.15) = 1.96
Thank you I left out the .15 and sqrt. I have a lot of problems with the standard deviation and not sure why. Is there a simple formula to use????
To find the mean of a binomial random variable, we can use the formula:
mean = n * p
where:
- n is the number of trials
- p is the probability of success in each trial
In this case, we are given that n = 30 and p = 0.85.
Substituting these values into the formula, we get:
mean = 30 * 0.85 = 25.5
Therefore, the mean of the binomial random variable is 25.5.
To find the standard deviation of a binomial random variable, we can use the formula:
standard deviation = sqrt(n * p * (1 - p))
Using the same values of n = 30 and p = 0.85:
standard deviation = sqrt(30 * 0.85 * (1 - 0.85))
Calculating this expression, we get:
standard deviation = 3.085156
Rounding this to two decimal places, the standard deviation is approximately 3.09.