A binomial experiment consists of 9 independent trials. The probability of success in each is 0.4.
a) Using the tables findP(X(less than or equal to symbol) 3).
b) Find the mean and standard deviation of the random variable associated with this experiment.
a) I used the table in the back of my textbook for this.
I think its : p(x+0) + p (x+1) + p(x+2)+ p(x+3)
= 0.010 + 0.060 + 0.161+ 0.251 = 0.482
b) Mean = np = 9 * 0.4 = 3.6
SD = Sq root of 9*0.4*0.4= 1.47
**Also I can only use the np formula and square root of npq for binomials right?
To solve this problem, you correctly used the probability mass function (PMF) of a binomial distribution to find the probability of the random variable X being less than or equal to 3:
P(X ≤ 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)
Using the binomial distribution table in your textbook, you found the corresponding probabilities for each value of X and added them together. Your calculation is correct, and the result of P(X ≤ 3) = 0.482.
For part b) of the question, you are also correct. The mean (μ) of a binomial distribution is given by the formula np, where n is the number of trials and p is the probability of success in each trial. In this case, the mean is calculated as 9 * 0.4 = 3.6.
The standard deviation (σ) of a binomial distribution can be found using the formula √(npq), where q represents the probability of failure in each trial, which is equal to 1 - p. Therefore, the standard deviation is calculated as √(9 * 0.4 * 0.6) = 1.47.
To clarify your final question, the formulas np and √(npq) are indeed used specifically for binomial distributions. These formulas represent the mean and standard deviation of the binomial distribution, respectively.