In a binomial experiment with n=300 and p=0,5 find(p> 0,6)
To find the probability that p is greater than 0.6 in a binomial experiment with n=300 and p=0.5, we can use the normal approximation to the binomial distribution.
First, we find the mean and standard deviation of the binomial distribution:
Mean = n * p = 300 * 0.5 = 150
Standard deviation = sqrt(n * p * (1-p)) = sqrt(300 * 0.5 * 0.5) = sqrt(75) = 8.66
Next, we standardize the probability of interest:
z = (0.6 - 0.5) / 8.66 = 0.1155
Using a z-table or calculator, we find that the z-score of 0.1155 corresponds to a probability of approximately 0.4545.
Therefore, the probability that p is greater than 0.6 in a binomial experiment with n=300 and p=0.5 is 0.4545.