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The time spent waiting in the line is approximately normally distributed. The mean waiting time is...

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 1 minute. Find the probability that a person will wait for more than 7 minutes. Round your answer to four decimal places

Math   Statistics-And-Probability   
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Answer #1

Solution :

Given, X follows Normal distribution with,

   = 6

   = 1

Find P(X > 7)

P(X > 7) = P [(X - )/ >  (7 - )/]

= P[Z > (7 - 6)/1]

= P[Z > 1.00]

= 1 - P[Z < 1.00]

= 1 - 0.8413 ......... ( use z table)

= 0.1587

Answer :    P(X > 7) = 0.1587

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