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The time spent waiting in the line is approximately normally distributed. The mean waiting time is 7 minutes and the standard deviation of the waiting time is 1 minute. Find the probability that a person will wait for more than 6 minutes.

User Cubesnyc
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Final answer:

To find the probability that a person will wait for more than 6 minutes, calculate the z-score and use the standard normal distribution. The probability is approximately 84.13%.

Step-by-step explanation:

To find the probability that a person will wait for more than 6 minutes, we need to calculate the z-score and use the standard normal distribution. The z-score is calculated by subtracting the mean (7 minutes) from the value (6 minutes) and dividing by the standard deviation (1 minute). So, the z-score is (6 - 7) / 1 = -1.

We can then look up the cumulative probability of the z-score using a standard normal distribution table or calculator. The probability that a person will wait for more than 6 minutes is the complement of the cumulative probability up to the z-score value. In this case, it is 1 minus the cumulative probability of -1.

Using a standard normal distribution table, we can find that the cumulative probability of -1 is 0.1587. Therefore, the probability that a person will wait for more than 6 minutes is 1 - 0.1587 = 0.8413, or approximately 84.13%.

User JFAP
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