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The duration of flights is normally distributed with a mean of 6 hours and standard deviation...

The duration of flights is normally distributed with a mean of 6 hours and standard deviation of 45 minutes. what percentage of flights can be expected to take off between 7 and 8

Math   Statistics-And-Probability   
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Answer #1

Solution :

Given that ,

mean = = 6 hours ( 360 minutes)

standard deviation = = 45 minutes

7 = 420 minutes

8 = 480 minutes

P(420 < x < 480) = P[(420 - 360)/45 ) < (x - ) /  < (480 - 360) / 45) ]

= P(1.33 < z < 2.67)

= P(z < 2.67) - P(z < 1.33)

Using z table,

= 0.9962 - 0.9082

= 0.0880

The percentage is = 8.80%

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