Answer:
a) The probability that a randomly selected college student will find a parking spot in the library parking lot in less than 3 minutes = 0.309
b) Check the beginning of Explanation for which type of dustribution this is.
Step-by-step explanation:
A distribution with the mean given and the spread around the mean (standard deviation) given, is a normal distribution. Especially as it shows that the distribution is symmetric around the mean.
To find the probability that a randomly selected college student will find a parking spot in the library parking lot in less than 3 minutes.
We first standardize '3 minutes'.
The standardized score is the value minus the mean then divided by the standard deviation.
z = (x - μ)/σ = (3 - 3.5)/1 = - 0.5
probability that a randomly selected college student will find a parking spot in the library parking lot in less than 3 minutes.
P(x < 3) = P(z < -0.5)
We'll use data from the normal probability table for these probabilities
P(x < 3) = P(z < -0.5) = 1 - P(z ≥ - 0.5) = 1 - P(z ≤ 0.5) = 1 - 0.691 = 0.309.