the mean of a normal distribution is 20 and 9% of the values exceed 25. Find the SD of the distribution (area under normal curve between z=0 and z=1.34 is 0.41)
Answers
Answer:
Step-by-step explanation:
Once we have the general idea of the Normal Distribution, the next step is to learn how to find areas under the curve. We'll learn two different ways - using a table and using technology.
Since every normally distributed random variable has a slightly different distribution shape, the only way to find areas using a table is to standardize the variable - transform our variable so it has a mean of 0 and a standard deviation of 1. How do we do that? Use the z-score!
Z = x - μ
σ
As we noted in Section 7.1, if the random variable X has a mean μ and standard deviation σ, then transforming X using the z-score creates a random variable with mean 0 and standard deviation 1! With that in mind, we just need to learn how to find areas under the standard normal curve, which can then be applied to any normally distributed random variable.