Find and Interpret the Area under a Normal Curve
-The length of time it takes college students to find a parking spot in the library parking lot follows a normal distribution with a mean of 3.5 minutes and a standard deviation of 1 minute. Find the probability that a randomly selected college student will take between 2.0 and 4.5 minutes to find a parking spot in the library lot.
A) $0.7745$
B) $0.4938$
C) $0.0919$
D) $0.2255$

Question

Find and Interpret the Area under a Normal Curve
-The length of time it takes college students to find a parking spot in the library parking lot follows a normal distribution with a mean of 3.5 minutes and a standard deviation of 1 minute. Find the probability that a randomly selected college student will take between 2.0 and 4.5 minutes to find a parking spot in the library lot. 
A) $0.7745$
B) $0.4938$
C) $0.0919$
D) $0.2255$

Quizplus · Accepted Answer

To find the probability that a time is between 2.0 and 4.5 minutes, we convert these times to z-scores using the formula $z = \frac{x - \mu}{\sigma}$, where $x$ is the value, $\mu$ is the mean, and $\sigma$ is the standard deviation. For 2.0 minutes, $z = \frac{2.0 - 3.5}{1} = -1.5$. For 4.5 minutes, $z = \frac{4.5 - 3.5}{1} = 1.0$. Looking these z-scores up in a standard normal distribution table or using a calculator, we find the probabilities corresponding to these z-scores and subtract the smaller from the larger to find the area (probability) between them. This calculation gives us approximately 0.7745, indicating a 77.45% chance a student will find a parking spot between 2.0 and 4.5 minutes.

Find and Interpret the Area Under a Normal Curve -The 0.77450.77450.7745

Find and Interpret the Area Under a Normal Curve
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