A
study of long-distance phone calls made from General Electric Corporate
Headquarters in Fairfield, Connecticut, revealed the length of the
calls, in minutes, follows the normal probability distribution. The mean
length of time per call was 3.70 minutes and the standard deviation was
0.60 minutes.

What fraction of the calls last between 3.00 and 5.50 minutes? (Round z-score computation to 2 decimal places and your final answer to 4 decimal places.)

Thank you for the opportunity to help you with your question!

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.

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.

Please let me know if you need any clarification. I'm always happy to answer your questions.

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?

Sep 23rd, 2015

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