scottie_000 said:Have you drawn yourself a small sketch of what the curve will look like in this case?
Remember that the mean is already at 12.
Also, since this is a continuous distribution, you need to find the probability that X is within a range of values:
P(0<=X<=12) = P(X<=12) - P(X<=0)
A normal distribution is a type of probability distribution that is often used in statistics to describe a set of data. It is also known as a Gaussian distribution or bell curve because it has a characteristic shape that is symmetric and bell-shaped. In a normal distribution, the majority of the data points are clustered around the mean, with fewer points further away from the mean.
A variable is normally distributed if it follows a normal distribution, meaning that the data points are distributed around the mean in a symmetric, bell-shaped curve. This means that most of the data points are close to the mean, with fewer points further away from the mean. Variables that are normally distributed are often used in statistical analyses because they have certain properties that make them easier to work with.
The mean of a normally distributed variable is calculated by taking the sum of all the data points and dividing it by the total number of data points. This is also known as the average or the arithmetic mean. In a normal distribution, the mean is often denoted by the symbol "μ" and is located at the center of the bell curve.
The mean is an important measure of central tendency in a normal distribution because it represents the average value of the data points. It is also used to calculate other important measures such as the standard deviation, which is a measure of the spread of the data. In a normal distribution, the mean is also equal to the median and mode, making it a good representation of the entire dataset.
No, a variable cannot be normally distributed without having a specific mean. The mean is a defining characteristic of a normal distribution and is necessary for the data points to be symmetrically distributed around it. If a variable does not have a specific mean, it cannot be considered normally distributed.