(TCO B) Pharmacies continually monitor their prescription filling process. A loc

Question

(TCO B) Pharmacies continually monitor their prescription filling process. A local pharmacy has noted that the time to fill a prescription for a generic antibiotic is normally distributed, with a mean of 13.3 minutes and a standard deviation of 2.8 minutes.  

a. Find the probability that a prescription for a generic antibiotic takes at least 10 minutes to fill.
b. Find the probability that the prescription for a generic antibiotic takes between 12 and 15 minutes to fill.
c. The slowest 20% of prescription fills result in a special discount to the customer. How long must a prescription fill for a generic antibiotic take in order to qualify for this discount?

Explanation / Answer

mean = 13.3 , s = 2.8

a)

P(X > 10)
z = ( x - mean) / s
= ( 10 - 13.3) / 2.8
= -1.1786

we need to find P ( z > -1.1786)
P(X > 10) = P ( z > -1.1786) = 0.8807

b)
P(12 < X < 15)

(( 12 - 13.3 / 2.8) < Z < ( 15 -13.3/2.8))
( -0.4643 < z < 0.6071)
we need to find P (-0.4643 < z < 0.6071)

P(12 < X < 15) = P (-0.4643 < z < 0.6071) = 0.4069

c) z value for 20% = -0.84162

-0.84162 = ( x - 13.3) / 2.8
x = 10.9434

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