Question

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 6.5 minutes and a standard deviation of 1 minute.

a. Find the probability that it will take a randomly selected college student more than 4.0 minutes to find a parking spot in the library parking lot.

b. Find the probability that a randomly selected college student will find a parking spot in the library parking lot in less than 6.0 minutes.
c. Find the probability that a randomly selected college student will take between 5.0 and 7.5 minutes to find a parking spot in the library lot.

Answer 1

Solution :

a.

P(x > 4.0) = 1 - P(x < 4.0)

= 1 - P[(x - ) / < (4.0 - 6.5) / 1)

= 1 - P(z < -2.5)

= 1 - 0.0062

= 0.9938

Probability = 0.9938

b.

P(x < 6.0) = P[(x - ) / < (6.0 - 6.5) / 1]

= P(z < -0.5)

= 0.3085

Probability = 0.3085

c.

P(5.0 < x < 7.5) = P[(5.0 - 6.5)/ 1) < (x - ) /  < (7.5 - 6.5) / 1) ]

= P(-1.5 < z < 1)

= P(z < 1) - P(z < -1.5)

= 0.8413 - 0.0668

= 0.7745

Probability = 0.7745