Question 177721: A normally distributed population has a mean of 60 and a standard deviation of 6.
a. Compute the probability of a value between 60 and 69. _______
b. Compute the probability of a value between 51 and 66. ________
c. Compute the probability of a value less than 51. ________
d. Compute the probability of a value greater than 72. ________
Answer by EMStelley(208)   (Show Source):
You can put this solution on YOUR website! I will help you with part a) and you can work on the rest. The first step in trying to compute a probability like this is standardizing the values. Remember, this is done by subtracting the mean and dividing by the standard deviation. For example, 60 would be (60-60)/6=0 (the mean is always 0 standardized). Similarly, 69 would be (69-60)/6=1.5. So what the question is really asking is "what is the area under the normal curve between 0 and 1.5?" Well, if we use a table to look up 1.5, such as http://www.sjsu.edu/faculty/gerstman/EpiInfo/z-table.htm
we get that the area to the left of 1.5 is 0.9332, or 93.32%. But what we're looking for is just between 0 and 1.5. Remember that the normal curve is symmetrical about 0, so the area to the left of 0 is exactly half, or 0.5 (or 50%). So if we subtract 50% from 93.32%, we'll get the area in between 0 and 1.5. So the probability of a value between 60 and 69 is 43.32%. Hope that helps.
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