Answer:
0.7745 is the required probability.
Step-by-step 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:
[tex]z_{score} = \displaystyle\frac{x-\mu}{\sigma}[/tex]
P(college student will take between 5.0 and 7.5 minutes)
[tex]P(5.0 \leq x \leq 7.5)\\\\ = P(\displaystyle\frac{5.0 - 6.5}{1} \leq z \leq \displaystyle\frac{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\%[/tex]
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
