Calculating Probability of a Value Being in a Certain Range
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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.
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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.
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: ...
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