John's commute time to work during the week follows the normal probability distribution with a mean time of 26.7 minutes and a s

Question

3 years ago

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John's commute time to work during the week follows the normal probability distribution with a mean time of 26.7 minutes and a s

tandard deviation of 5.1 minutes. what is the probability that the commute time for a randomly selected day will be more than 30 minutes?

Mathematics

1 answer:

Galina-37 [17] · Answer 1 · 2022-03-06T18:50:38+03:00

A suitable probability calculator will tell you that probabilty is about 25.9%.

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The normalcdf function on this calculator gives an area between a lower and upper limit. If the upper limit is more than about 8 standard deviations above the mean, the 10th decimal place is unaffected. Since the standard deviation here is about 5, we need to have an upper limit that is about 40 above the mean of about 30. We have chosen 80 as a nice round number and to give a little more margin.