Question 933040: The length of time it takes college students to find a parking spot in the library parking lot follows a normal distribution with mean of 7.0 minutes and a standard deviation of 1 minutes. Find the probability that a randomly selected college student will find a parking spot in the library parking lot in less than 6.5 minutes.
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! Step 1) Convert the raw score x = 6.5 to a z-score (mu = 7, sigma = 1)
z = (x-mu)/sigma
z = (6.5-7)/1
z = -0.5
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Step 2) Use a calculator or a table to find the area under the curve to the left of z = -0.5. I'm using the table.
Using the table, I get P(Z < -0.5) = 0.3085
So, P(X < 6.5) = 0.3085
So the probability that a randomly selected college student will find a parking spot in the library parking lot in less than 6.5 minutes is approximately 0.3085
Final Answer: 0.3085 (this is equivalent to roughly 30.85%)
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