The cost of treatment per patient for a certain medical problem was modelled by one insurance company as a normal random variable with mean $775 and a standard deviation of $150. What is the probability that the treatment cost of a patient is less than $1,000, based on this model?
Answers
Given : The cost of treatment per patient for a certain medical problem modeled by insurance company as a normal random variable with mean $775 and a standard deviation of $150
To find : probability that the treatment cost of a patient is less than $1,000 , based on given model
Solution:
Mean = 775$
Standard Deviation = 150 $
Z score = ( Value - Mean)/Standard Deviation
Value = 100 $
Z = (1000 - 775)/150
=> Z = 225/150
=> Z = 1.5
Refer attach Z score table
Z = 1.5
=> 0.9332
=> Probability that the treatment cost of a patient is less than $1,000, = 0.9332
0.9332 is the probability that the treatment cost of a patient is less than $1,000
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