X is a random variable following binomial distribution with mean 2.4 and variance 1.44 find
Q.4. X is a random variable following binomial distribution with mean 2.4 and variance 1.44 find P[X>5]
X is a random variable following binomial distribution with mean 2.4 and variance 1.44 find P[X>5]
If n is large enough, binomial distribution approximates a normal distribution.
Z = (score-mean)/SD
√variance = SD
Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion/probability related to the Z score.
To find the value of X, we need to know which specific value we are interested in (e.g., finding the probability of X = k, or finding the cumulative probability for X ≤ k).
However, since you have provided the mean (μ = 2.4) and variance (σ^2 = 1.44) of the binomial distribution, we can use these values to calculate the parameters of the distribution.
In a binomial distribution, the mean and variance are related to the number of trials (n) and the probability of success (p) in each trial.
The mean (μ) of a binomial distribution with n trials and probability of success p is given by μ = n * p.
From the given information, we have μ = 2.4. However, we don't know the values of n or p yet.
The variance (σ^2) of a binomial distribution with n trials and probability of success p is given by σ^2 = n * p * (1 - p).
From the given information, we have σ^2 = 1.44. Again, we don't know the values of n or p yet.
Solving these two equations simultaneously will give us the values of n and p.
Step 1: Solve for p using the variance equation:
1.44 = n * p * (1 - p)
Step 2: Substitute the value of p obtained in Step 1 into the mean equation:
2.4 = n * p
By solving these two equations simultaneously, we can find the values of n and p.
Once we obtain the values of n and p, we can use the binomial distribution formula or a probability calculator to find the desired probabilities or values of X.
Please provide additional information or clarify your question if you have a specific value of X you are interested in or if you want to find the values of n and p using the mean and variance.