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Dave drives to work each morning at about the same time. His commute time is normally distributed with a mean of 38 minutes and a standard deviation of 5 minutes. The percentage of time that his commute time exceeds 44 minutes is equal to the area under the standard normal curve that lies to the ___ of ___.

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Answer:

Right of z = 1.2

Step-by-step explanation:

Population mean (μ) = 38 minutes

Standard deviation (σ) = 5 minutes

The z-score for any given time X is described by:

[tex]z=\frac{X-\mu}{\sigma}[/tex]

For X = 44 minutes:

[tex]z=\frac{44-38}{5}\\z= 1.2[/tex]

Z-scores to the right of 1.2 will represent times over 44 minutes.

Therefore, the percentage of time in which Dave's commute will exceed 44 minutes is the area under the standard normal curve that lies to the right of z=1.2

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