Medication used to treat a certain condition is administered by syringe. The target dose in a particular application is μ. Because of the variations in the syringe, in reading the scale, and in mixing the fluid suspension, the actual dose administered is normally distributed with mean μ and variance σ². a) What is the probability that the dose administered differs from the mean μ by less than σ? b) If X represents the dose administered, find the value of z so that P(X < μ + zσ) = 0.90. c) If the mean dose is 10 mg, the variance is 2.6 mg², and a clinical overdose is defined as a dose larger than 15 mg, what is the probability that a patient will receive an overdose?

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Medication used to treat a certain condition is administered by syringe. The target dose in a particular application is μ. Because of the variations in the syringe, in reading the scale, and in mixing the fluid suspension, the actual dose administered is normally distributed with mean μ and variance σ². a) What is the probability that the dose administered differs from the mean μ by less than σ? b) If X represents the dose administered, find the value of z so that P(X < μ + zσ) = 0.90. c) If the mean dose is 10 mg, the variance is 2.6 mg², and a clinical overdose is defined as a dose larger than 15 mg, what is the probability that a patient will receive an overdose?

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