Normal distribution can also be known as Gaussian distribution. In statistics, the normal distributions are used to represent real-valued random variables with unknown distributions. Refer the below normal distribution examples and solutions and calculate gaussian distribution to compute the cumulative probability for any value
Let us consider the Gaussian distribution example: The time taken to assemble a car in a certain plant is a random variable having a normal distribution of 30 hours and a standard deviation of 4 hours. What is the probability that a car can be assembled in a period of time greater than 21 hours?
We can calculate the normal distribution using the given formula.
Substituting the values in the formula,
Gaussian Distribution Z = (21 - 30) / 4 = - 2.25 P(x > 21) = P(z > -2.25) Looking up the z-score in the z-table, we get 1 – 0.0122 = 0.9878
Therefore, the value of Normal Distribution is 0.9878.
Refer the below Gaussian distribution worked example. A large group of students took a test in Physics and the final grades have a mean of about 70 and a standard deviation of 10. If we can approximate the distribution of these grades by a normal distribution, what percent of the students should fail the test (i.e) less than 60?
Substituting the values in the above given formula,
Normal Distribution Z = (60 - 70) / 10 z = -1 P(x < 60) = P(z < -1) Looking up the z-score in the z-table, we get 1 - 0.8413 = 0.1587
Therefore, Normal Distribution is 0.1587.