How likely is the intervention program to be needed?

A First Course in Probability (10th Edition)
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ISBN:9780134753119
Author:Sheldon Ross
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Chapter1: Combinatorial Analysis
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Let X be the TSH level in an individual. It is assumed that X has an exponential distribution with a mean of 3 µIU /mL. A sample of 12 workers from a logging company is taken. If more than half of the individuals in the sample have TSH levels greater than 4.8 µUI /mL, an intervention program is carried out with the total number of workers in the company. How likely is the intervention program to be needed?

a) 0,004

b) 0,006

c) 0,086

d) 0,005

e) 0,003

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Let X be the TSH level in an individual. It is assumed that X has an exponential distribution with a mean of 3 µIU /mL. A sample of 12 workers from a logging company is taken

Here use poission distribution and binomial distribution 

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