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: 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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