Can a normal distribution always be used to approximate a binomial distribution explain your answer?

No, we cannot always approximate probabilities for binomial distributions using a normal distribution.

How do you know if a problem is probability distribution?

It has the following properties: The probability of each value of the discrete random variable is between 0 and 1, so 0 ≤ P(x) ≤ 1. The sum of all the probabilities is 1, so ∑ P(x) = 1. Yes, this is a probability distribution, since all of the probabilities are between 0 and 1, and they add to 1.

Is normal distribution A continuous probability distribution?

Continuous probability distribution: A probability distribution in which the random variable X can take on any value (is continuous). The normal distribution is one example of a continuous distribution.

Do you think that the normal distribution can approximate the distribution of a binomial variable?

Recall that if X is the binomial random variable, then X∼B(n,p). The shape of the binomial distribution needs to be similar to the shape of the normal distribution. Then the binomial can be approximated by the normal distribution with mean μ=np and standard deviation σ=√npq.

How do you determine if you can use normal approximation?

Step 2: Figure out if you can use the normal approximation to the binomial. If n * p and n * q are greater than 5, then you can use the approximation: n * p = 310 and n * q = 190. These are both larger than 5, so you can use the normal approximation to the binomial for this question.

Can a probability distribution be negative?

The probability of the outcome of an experiment is never negative, although a quasiprobability distribution allows a negative probability, or quasiprobability for some events.

What makes the normal distribution a probability distribution?

Normal distribution, also known as the Gaussian distribution, is a probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean. In graph form, normal distribution will appear as a bell curve.

Is normal probability distribution discrete or continuous?

The normal distribution, which is continuous, is the most important of all the probability distributions. Its graph is bell-shaped. This bell-shaped curve is used in almost all disciplines. Since it is a continuous distribution, the total area under the curve is one.