What is based on the normal curve distribution

What percent of the data is less than 5? A normal distribution is symmetric about the mean. So, half of the data will be less than the mean and half of the data will be greater than the mean. The life of a fully-charged cell phone battery is normally distributed with a mean of 14 hours with a standard deviation of 1 hour. What is the probability that a battery lasts at least 13 hours?

The mean is 14 and the standard deviation is 1. The interval from 13 to 14 hours represents one standard deviation to the left of the mean. The average weight of a raspberry is 4. What is the probability that a randomly selected raspberry would weigh at least 3. The mean is 4. So, the interval 3.

In addition, The larger the standard deviation, the wider the graph. The smaller it is, the narrower the graph. Percentiles represent the area under the normal curve, increasing from left to right.

Each standard deviation represents a fixed percentile, and follows the empirical rule. Note that the 0 th percentile falls at negative infinity and the th percentile at positive infinity. The standard normal distribution is a normal distribution with a mean of 0 and a standard deviation of 1.

Since the standard deviation is 1, this represents the probability that a normal distribution is between 2 standard deviations away from the mean. From the empirical rule , we know that this value is 0. Unfortunately, in most cases in which the normal distribution plays a role, the mean is not 0 and the standard deviation is not 1. It can be said to provide an assessment of how off-target a process is operating. It requires knowing the population parameters, not the statistics of a sample drawn from the population of interest.

However, knowing the true standard deviation of a population is often unrealistic except in cases such as standardized testing, where the entire population is measured. In cases where it is impossible to measure every member of a population, the standard deviation may be estimated using a random sample.

Assuming that the height of women in the US is normally distributed with a mean of 64 inches and a standard deviation of 2. Part one : Since the height of women follows a normal distribution but not a standard normal, we first need to standardize.

This table can be seen below. Standardizing these values we obtain:. To calculate the probability that a variable is within a range in the normal distribution, we have to find the area under the normal curve.

Same as in the process of standardization discussed in the previous section. For example, if we want to know the probability that a variable is no more than 0. The intersection of the 6 th row and 2 nd column is 0. This tells us that there is a Notice that for 0. This shows us that there is equal probability of being above or below the mean. This problem essentially asks what is the probability that a variable is less than 1.

On the table of values, find the row that corresponds to 1. This gives us a probability of 0. This problem essentially asks what is the probability that a variable is MORE than 1. However, this is the probability that the value is less than 1. Since all the probabilities must sum to However, we can use the symmetry of the distribution, as follows:. Privacy Policy. Skip to main content. Continuous Random Variables. Search for:. The Normal Curve. Continuous Probability Distributions A continuous probability distribution is a representation of a variable that can take a continuous range of values.

The empirical rule is often referred to as the three-sigma rule or the The empirical rule allows researchers to calculate the probability of randomly obtaining a score from a normal distribution. This means there is a Statistical software such as SPSS can be used to check if your dataset is normally distributed by calculating the three measures of central tendency.

If the mean, median and mode are very similar values there is a good chance that the data follows a bell-shaped distribution SPSS command here. Normal distributions become more apparent i. You can also calculate coefficients which tell us about the size of the distribution tails in relation to the bump in the middle of the bell curve. McLeod, S. Introduction to the normal distribution bell curve. Toggle navigation. In a sense, we need to know how far a given value is from the mean and the probability of having values less than this.

And, of course, we would want to have a way of figuring this out not only for BMI values in a population of males with a mean of 29 and a standard deviation of 6, but for any normally distributed variable. So, what we need is a standardized way of evaluating any normally distributed data so that we can compute the probability of observing the results obtained from samples that we take.

We can do all of this fairly easily by using a "standard normal distribution. What is the probability that a randomly selected male from this population would have a BMI less than 30? This provides us with a way of standardizing how far a given observation is from the mean for any normal distribution, regardless of its mean or standard deviation.

Now what we need is a way of finding the probabilities associated various Z-scores. This can be done by using the standard normal distribution as described on the next page.

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