undefinedWhen Zahra commutes to work, the amount of time it takes her to arrive is normally distributed with a mean of 28 minutes and a standard deviation of 4.5 minutes. What is the probability that on a given day, her commute will be longer than 38 minutes, to the nearest thousandth?
To find the probability that her commute will be longer than 38 minutes, we need to calculate the z-score first.
Z = (X - μ) / σ
Z = (38 - 28) / 4.5
Z = 2.2222...
Next, we look up the z-score in the standard normal distribution table to find the probability associated with a z-score of 2.22, which is approximately 0.9861.
Therefore, the probability that Zahra's commute will be longer than 38 minutes is 1 - 0.9861 = 0.0139.
Rounded to three decimal places, the probability is approximately 0.014.