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Sta220 Section 4.4-4.5 Area under the curve always equals __________. Example Find the probability that the standard normal random variable z falls between -1.33 and +1.33. Solution: Example Find the probability that the standard normal random variable z falls between 1.00 and 2.50. Solution: Example Suppose the random variable x is best described by a normal distribution with 𝜇 = 25 and 𝜎 = 5. Find the z-score that corresponds to the x value: x = 37.5. Solution: Example Find a value 𝒛𝟎 of the standard normal random variable z such that: a) 𝑷(𝒛 ≤ 𝒛𝟎 ) = 𝟎. 𝟎𝟒𝟎𝟏 b) 𝑷(−𝒛𝟎 ≤ 𝒛 ≤ 𝒛𝟎 ) = . 𝟗𝟎 Example Suppose x is a normal distributed random variable with 𝝁 = 𝟑𝟎 and 𝝈 = 𝟖. Find a value 𝒙𝟎 of the random variable x such that: a) 𝑷(𝒙 ≥ 𝒙𝟎 ) = . 𝟏. b) 80% of the values x are less than 𝒙𝟎 . Example Assume that the length of time, x, between charges of a cellular phone is normally distributed with a mean of 10 hours and a standard deviation of 1.5 hours. Find the probability that the cell phone will last between 8 and 12 between charges. Solution Problem 4.22 Suppose that the scores x on a college entrance examination are normally distributed with a mean of 550 and the standard deviation of 100. A certain prestigious university will consider for admission only those applicants whose scores exceed the 90th percentile of the distribution. Find the minimum score an applicant must achieve in order to receive consideration for admission to the university.