In a binomial distribution:
A) the random variable X is continuous.
B)the probability of event of interest (pie symbol)is stable from trail to trial
C) the number of trials n must be at least 30
D) the results of one trial are dependent on the results of the others.
I narrowed it down to A or B
B is the answer
Compute the standard deviation mc006-1.jpg for ages of British nurses in 1851 if the mean mc006-2.jpg is 53.75. Assume that the table below shows the age distribution of nurses in Great Britain in 1851. Round your answer to nearest hundredth.
Between A and B, the correct answer is B) the probability of the event of interest (π symbol) is stable from trial to trial.
In a binomial distribution, the random variable X represents the number of successes in a fixed number of independent trials. It is a discrete random variable, meaning it can only take on specific values.
The probability of success, denoted by π, is constant from trial to trial in a binomial distribution. This means that the probability of the event of interest remains the same throughout the trials.
Option A, "the random variable X is continuous," is incorrect because a binomial distribution deals with discrete random variables, not continuous ones.
Option C, "the number of trials n must be at least 30," is not a requirement for a binomial distribution. The number of trials can be any positive integer.
Option D, "the results of one trial are dependent on the results of the others," is also incorrect. In a binomial distribution, the trials are assumed to be independent, meaning the outcome of one trial does not affect the outcome of the others.
To determine whether A) the random variable X is continuous or B) the probability of the event of interest is stable from trial to trial in a binomial distribution, let's break down each option and find the correct answer:
A) The random variable X is continuous:
A binomial distribution deals with discrete random variables, which means the outcome can only be certain distinct values. Therefore, option A is incorrect as the random variable X in a binomial distribution is not continuous.
B) The probability of the event of interest is stable from trial to trial:
In a binomial distribution, the probability of the event of interest remains constant or stable from trial to trial. This is because each trial is assumed to be independent, and the probability of success (event of interest) remains the same for each trial. Therefore, option B is correct.
So the correct answer is B) the probability of the event of interest is stable from trial to trial in a binomial distribution.