Fightfish said:From |X-80| <= 10, you can get -10 <= (X-80) <= 10, -1 <= Z <= 1
We also know that P(Z<-1) = P(Z>1) due to symmetry. Hope that helps.
Yup.needhelp83 said:I do understand partially. I remember this from just basic algebra. Afterwards, would I solve for P(70 <= X <= 90) where I added 80 to both sides?
statdad said:Check your final calculation - you have a glaring error.
A normal random variable is a type of continuous probability distribution that is often used in statistics. It is also known as a Gaussian distribution and is characterized by a bell-shaped curve. It is commonly used to model real-world phenomena such as height, weight, and test scores.
A normal random variable is different from other types of random variables in that it is continuous, meaning it can take on any value within a specific range. Other types of random variables, such as discrete random variables, can only take on certain values.
The mean and standard deviation are important parameters in a normal random variable because they determine the shape and location of the bell-shaped curve. The mean is the center of the curve and the standard deviation controls the spread of the curve. Together, these parameters provide important information about the distribution of the data.
The probability of a normal random variable is calculated using a formula called the probability density function (PDF). This formula takes into account the mean, standard deviation, and the specific value of the random variable to determine the likelihood of that value occurring in the distribution.
The central limit theorem states that the sum of a large number of independent and identically distributed random variables will tend towards a normal distribution, regardless of the underlying distribution of the individual variables. This means that many real-world phenomena can be approximated by a normal random variable, making it a useful tool in statistics and data analysis.