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Calculating Probability of a Value Being in a Certain Range

A normal distribution has a mean of 50 and a standard deviation of 4.

a. Compute the probability of a value between 44.0 and 55.0.
b. Compute the probability of a value greater than 55.0.
c. Compute the probability of a value between 52.0 and 55.0.

Solution Preview

Whenever we want to find probabilities we need to use tables at the back of a stats book. Unfortunately they contain probabilities for STANDARD normal distribution (i.e. mean = 0, variance =1). Because we have a non-STANTARD distribution (but it's still normal), we will need to STANDARDIZE it.

The procedure for that is: we compute z statistic, which is the standardized equivalent for any value from our distribution. So,

z = (value - mean)/st.deviation of original statistic

So, if we weant to find the probability of a value greater than 55, then we will compute z as

z = (55-50)/4 = 1.25

Now, we're looking for area under stand.normal curve to the RIGHT of 1.25 (re: ...

Solution Summary

This solution contains both a general-level description of the solution and step-by-step calculations required to arrive at the probability of a value being in a specific range under normal distribution. The solution also explains how to use the tables at the back of standard statistics books to find the required probabilities.

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