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 55 minutes and a standard deviation of 1 minute. Find the probability that a randomly selected college student will take between 3.53.5 and 66 minutes to find a parking spot in the library lot.

Answer: 0.7745Step-by-step explanation:Given : The length of time it takes college students to find a parking spot in the library parking lot follows a normal distribution with [tex]\mu=5\text{ minutes}[/tex]Standard deviation : [tex]\sigma=1\text{ minute}[/tex]Let x be the random variable that represents the length of time it takes college students to find a parking spot .Z-score : [tex]z=\dfrac{x-\mu}{\sigma}[/tex]For x = 3.5 minutes[tex]z=\dfrac{3.5-5}{1}=-1.5[/tex]For x = 6 minutes[tex]z=\dfrac{6-5}{1}=1[/tex]Now, the probability that a randomly selected college student will take between 3.5 and 6 minutes to find a parking spot in the library lot will be :-[tex]P(3.5<X<6)=P(-1.5<z<1)\\\\=P(z<1)-P(z<-1.5)\\\\= 0.8413447-0.0668072=0.7745375\approx0.7745[/tex]Hence, the  probability that a randomly selected college student will take between 3.5 and 6 minutes to find a parking spot in the library lot will be 0.7745.