Question

The time it takes to travel from home to the office is normally distributed with mean = 20 minutes and standard deviation = 4 minutes. What is the probability that the trip takes more than 32 minutes?

Answer 1

Using the z-score calculation, the probability of the trip from home to the office taking more than 32 minutes is determined to be 0.0013 or 0.13%.

Step-by-step explanation:

To calculate the probability that the trip takes more than 32 minutes, given the time it takes is normally distributed with a mean of 20 minutes and a standard deviation of 4 minutes, we first standardize the 32-minute value into a z-score. To find the z-score, subtract the mean from the value, and divide by the standard deviation:

Z = (X - μ) / σ
Z = (32 - 20) / 4 = 12 / 4 = 3
A z-score of 3 indicates that 32 minutes is 3 standard deviations above the mean. To find the probability that the trip takes more than 32 minutes, we look up the corresponding probability for a z-score of 3 in the standard normal distribution table, which gives us a probability of about 0.9987 that a value is less than 32 minutes. Therefore, the probability of a trip taking more than 32 minutes is 1 - 0.9987 = 0.0013, or 0.13%.
This result shows that there is a very small probability that it will take more than 32 minutes to commute. Such calculations are useful for planning and can help set expectations for journey times.