Final answer:
To find the probability that it takes between 8 and 12 minutes to find a parking space at 9:00 a.m., we calculate the probability that it takes at least 8 minutes and subtract the probability that it takes more than 12 minutes. The probability is 0.6826. Option d
Step-by-step explanation:
To find the probability that it takes between 8 and 12 minutes to find a parking space at 9:00 a.m., we need to calculate the probability that it takes at least 8 minutes and subtract the probability that it takes more than 12 minutes.
The length of time it takes to find a parking space at 9 a.m. follows a normal distribution with a mean of 5 minutes and a standard deviation of 2 minutes.
Using the z-score formula, we can convert the time values to z-scores and then use the standard normal distribution table to find the probabilities.
The probability that it takes at least 8 minutes is 0.8413 and the probability that it takes more than 12 minutes is 0.1587. Subtracting these probabilities, we get:
Probability = 0.8413 - 0.1587 = 0.6826 . Option d