Question

The length of time it takes a college student to find a parking spot in the student center parking lot follows a non-normal distribution with a mean of 3.0 minutes and a standard deviation of 1 minute. Find the probability that the mean time to find a parking spot in the student center parking lot is less than 2.0 minutes for a randomly selected sample of 100 students

Answer #1

Answer: The length of time it takes a college student to find a parking spot in the student center parking lot follows a non-normal distribution with a mean of 3.0 minutes and a standard deviation of 1 minute. Find the probability that the mean time to find a parking spot in the student center parking lot is less than 2.0 minutes for a randomly selected sample of 100 students.

Solution:

Mean, μ = 3.0

Standard deviation, σ = 1

Sample size, n =100

P(X < 2) = P(x - μ)/σ < (2-μ)/ σ)

P(X < 2) = P(z < (2-3)/1/√100)

P(X < 2) = P(z < -1)

= 1 - P(z > 1)

= 1 - 0.8413

P(X < 2) = 0.1587

Therefore, the probability that the mean time to find a parking spot in the student center parking lot is less than 2.0 minutes for a randomly selected sample of 100 students = 0.1587

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