# Can a normal distribution be used to approximate discrete probability distributions?

## Can a normal distribution be used to approximate discrete probability distributions?

The Normal Distribution (continuous) is an excellent approximation for such discrete distributions as the Binomial and Poisson Distributions, and even the Hypergeometric Distribution.

## Can there be normal distribution for discrete data?

Normal distribution is strictly only applicable for data that is continuous though in some cases we can use the normal distribution to approximate data that is discrete.

**Is a discrete distribution a normal distribution?**

Unlike the normal distribution, which is continuous and accounts for any possible outcome along the number line, a discrete distribution is constructed from data that can only follow a finite or discrete set of outcomes.

**How do you approximate normal distribution?**

Then the binomial can be approximated by the normal distribution with mean μ=np and standard deviation σ=√npq. Remember that q=1−p. In order to get the best approximation, add 0.5 to x or subtract 0.5 from x (use x+0.5 or x−0.5).

### What is N in normal distribution?

The standard normal distribution is N(0,1); i.e., the normal distribution with mean 0 and variance 1. Probabilities for any normal distribution N(µ, σ2 ) can be found from a table for N(0,1).

### Is a normal 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.

**Is the distribution a discrete probability distribution?**

Note: With a discrete probability distribution, each possible value of the discrete random variable can be associated with a non-zero probability. Thus, a discrete probability distribution can always be presented in tabular form….Discrete Probability Distributions.

Number of heads | Probability |
---|---|

2 | 0.25 |

**How do you know if a distribution is discrete probability?**

A discrete probability distribution lists each possible value that a random variable can take, along with its probability. 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.

## What are four common types of continuous distribution?

Other continuous distributions that are common in statistics include:

- Beta distribution,
- Cauchy distribution,
- Exponential distribution,
- Gamma distribution,
- Logistic distribution,
- Weibull distribution.

## Can we approximate P̂ by a normal distribution Why?

Can we approximate p̂ by a normal distribution? Why? (Use 2 decimal places.) np = 58 ∗ 0.21 = 12.18 > 5 nq = 58 ∗ 0.79 = 45.82 > 5 and p̂ can be approximated by a normal random variable because > 5 > 5. Answer: yes; because > 5 > 5.

**What is an approximately normal distribution?**

Intelligence test scores follow an approximately normal distribution, meaning that most people score near the middle of the distribution of scores. For example, on the IQ scale, about two-thirds of all scores fall between IQs of 85 and 115, and about 95% of scores fall between 70 and 130.