Question

the length of time it takes college students to find a parking spot in the library lot follows a normal distribution with a mean of 6.5 minutes and a standard deviation of 1 minute. find the probability that a randomly selected college student will take between 5.0 and 7.5 minutes to find a parking lot in the library lot

Answer 1

0.7745 is the required probability.

Explanation:

We are given the following information in the question:

Mean, μ = 6.5 minutes

Standard Deviation, σ = 1 minute

We are given that the distribution of length of time is a bell shaped distribution that is a normal distribution.

Formula:

`z_(score) = \displaystyle(x-\mu)/(\sigma)`

P(college student will take between 5.0 and 7.5 minutes)

`P(5.0 \leq x \leq 7.5)\\\\ = P(\displaystyle(5.0 - 6.5)/(1) \leq z \leq \displaystyle(7.5-6.5)/(1))\\\\ = P(-1.5 \leq z \leq 1)\\\\= P(z \leq 1) - P(z < -1.5)\\\\= 0.8413 - 0.0668 =0.7745 = 77.45\%`

0.7745 is the probability that a randomly selected college student will take between 5.0 and 7.5 minutes to find a parking lot in the library lot