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the time spent waiting in the line is approximately normally distributed. the mean waiting time is 6 minutes and the standard deviation of the waiting time is 2 minutes. find the probability that a person will wait for more than 4 minutes. round your answer to four decimal places.



Answer :

contexto1019

The probability that a person will wait for more than 4 minutes is 0.9332

[tex]\mu=7\text{ min}[/tex]

[tex]\sigma=2\text{ min}[/tex]

[tex]x=4\text{ min}[/tex]

Using the z-score formula,

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

Hence,

[tex]z=\frac{4-7}{2}[/tex]

[tex]z=\frac{-3}{2}[/tex]

[tex]z=-1.5[/tex]

From the z-scores table, the probability that a person will wait for more than 4 minutes is

[tex]z=-1.5[/tex]

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