Assume that it takes a college student an average of 5 minutes to find a parking spot in the main parking lot. Assume also that this time is normally distributed with a standard deviation of 2 minutes. Find the probability that a randomly selected college student will take between 2 and 6 minutes to find a parking spot in the main parking lot.
A) 0.1950
B) 0.4772
C) 0.4332
D) 0.6247

Question

Quizplus · Accepted Answer

To find the probability that a randomly selected college student will take between 2 and 6 minutes to find a parking spot, we use the Z-score formula: $Z = \frac{X - \mu}{\sigma}$, where $X$ is the value, $\mu$ is the mean, and $\sigma$ is the standard deviation. For $X = 2$ minutes, $Z = \frac{2 - 5}{2} = -1.5$. For $X = 6$ minutes, $Z = \frac{6 - 5}{2} = 0.5$. Looking up these Z-scores in the standard normal distribution table gives the probabilities of 0.0668 and 0.6915, respectively. The probability of taking between 2 and 6 minutes is the difference, 0.6915 - 0.0668 = 0.6247.

Assume That It Takes a College Student an Average of 5