The standard normal distribution is applied. The correct answer is c. It "spreads" a discrete value out over a range.
In a normal distribution, the values of mean, median and mode are equal. So, the point (ii) is correct in the context of a normal distribution curve. Also, the normal distribution curve or bell curve is symmetric about the line $X = \mu $ . So, the point (i) is also correct in this context.
The standard normal distribution is a normal distribution with mean μ = 0 and standard deviation σ = 1. The letter Z is often used to denote a random variable that follows this standard normal distribution.
To find the area to the right of a positive z-score, begin by reading off the area in the standard normal distribution table. Since the total area under the bell curve is 1 (as a decimal value which is equivalent to 100%), we subtract the area from the table from 1.
Expert-verified answer In a normal distribution graph, all the mean mode and median are equal. The total area under the normal distribution curve is 1 or 100%. It accurately shows how variable values are distributed. Therefore in the above statement, A discrete probability distribution is not true.
Normal distributions are symmetric around their mean. The mean, median, and mode of a normal distribution are equal. The area under the normal curve is equal to 1.0. Normal distributions are denser in the center and less dense in the tails.
The standard deviation is the measure of how spread out a normally distributed set of data is. It is a statistic that tells you how closely all of the examples are gathered around the mean in a data set. The shape of a normal distribution is determined by the mean and the standard deviation.
Why is it correct to say "a" normal distribution and "the" standard normal distribution? "The" standard normal distribution is used to describe one specific normal distribution (mean = 0, standard dev = 1) . "A" normal distribution is used to describe a normal distribution with any mean and standard deviation.
Q. Which is NOT true about the standard normal distribution? It is bell-shaped.
The standard normal distribution is a probability distribution, so the area under the curve between two points tells you the probability of variables taking on a range of values. The total area under the curve is 1 or 100%.
The total area under a standard normal distribution curve is 100% (that's “1” as a decimal). For example, the left half of the curve is 50%, or . 5. So the probability of a random variable appearing in the left half of the curve is .