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To make a probability calculation involving a normal distribution, it is helpful to translate the given distribution into the standard normal distribution so that the standard normal table can be used. The translatION is done by calculating a z-score for each of 3.00 and 5.00, then consulting a table to see what proportion of the area under the standard normal curve is between z(3) and z(5). The z-score formula is shown below.
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Then z(3) = (3 - 3.70) / 0.60 = -1.17 and z(5) = (5 - 3.70) / 0.60 = 2.17, so the fraction of calls lasting between 3 and 5 minutes is the proportion of the area under the STANDARD normal curve between
z = -1.17 and z = 2.17. That proportion can be looked up in a table or calculated online to be: 0.864 OR ABOUT 864 OUT OF 1000.
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I just entered that and it was incorrect.
Can you try this one
Cities with a population of more than 250,000 the mean one-way commute time to work is 24.3 minutes. The longest one-way travel time is in New York where the mean time is 38.8 minutes. Assume the distribution of travel times in New York follows the normal probability distribution and the standard deviation is 7.7 minutes.
ROUND ALL ANSWERS TO TWO DECIMAL PLACES
What % of commutes are less than 27 minutes
What % are between 27 & 35 minutes?What % are between 27 and 43 minutes?
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