Explore Westonci.ca, the leading Q&A site where experts provide accurate and helpful answers to all your questions. Get immediate and reliable answers to your questions from a community of experienced professionals on our platform. Connect with a community of professionals ready to help you find accurate solutions to your questions quickly and efficiently.
Sagot :
Answer:
1) probability that the average concentration of pollutants in the stream on a given day will exceed 85 mg/l is 0.0018
2) probability that a critical level of 95 mg/l will only be exceeded at the most one day in a given week (seven days) is 0.9993
Explanation:
Given the data in the question;
mean μ = 50 mg/l
standard deviation σ = 12 mg/l
we know that; x-score = x-μ / σ
1) probability that the average concentration of pollutants in the stream on a given day will exceed 85 mg/l
p( x > 85 ) = P( Z > 85-50 / 12 )
= P( Z > 35/12 )
= P( Z > 2.9166)
= P( Z > 2.92)
= 1 - P( Z > 2.92)
from z-score table; P( Z > 2.92) = 0.9982
= 1 - 0.9982
p( x > 85 ) = 0.0018
Therefore, probability that the average concentration of pollutants in the stream on a given day will exceed 85 mg/l is 0.0018
2) probability that a critical level of 95 mg/l will only be exceeded at the most one day in a given week (seven days). Assume that the pollutant concentrations between days are statistically independent.
p( x > 95 ) = p( Z > 95-50 / 12 )
= p( Z > 45 / 12 )
= p( Z > 3.75 )
= 1 - p( Z > 3.75 )
from z-score table; p( Z > 3.75 ) = 0.9999
= 1 - 0.9999
= 0.0001
Now; p = 0.0001 and n = ( week) = 7
x = number of days × exceeds 99 mg/l
x ¬ Binomial ( n =7 p = 0.0001 )
p(x ≤ 1) = p(x=0) + (p=1)
= ¹∑[tex]_{x=0}[/tex] [tex]^7C_x ( 0.0001)^x[/tex] [tex](0.9999)^{7-x}[/tex]
= [tex]^7C_0 ( 0.0001)^0[/tex] [tex](0.9999)^{7-0}[/tex]
= 7!/(0!(7-0)!) [tex]( 0.0001)^0[/tex] [tex](0.9999)^{7-0}[/tex]
= (1) ( 1 ) ( 0.9993 )
= 0.9993
Therefore, probability that a critical level of 95 mg/l will only be exceeded at the most one day in a given week (seven days) is 0.9993
We hope you found this helpful. Feel free to come back anytime for more accurate answers and updated information. Thank you for your visit. We're committed to providing you with the best information available. Return anytime for more. Your questions are important to us at Westonci.ca. Visit again for expert answers and reliable information.