Question
6-35 A recent study by an environmental watchdog determined that the amount of contaminants in Minnesota lakes (in parts per million) it has a normal distribution with a mean of 64 ppm and variance of 17.6. Assume that 35 lakes are randomly selected and sampled. Find the probability that the sample average of the amount of contaminants is a) Greater than 72 ppm. b) Between 64 and 72 ppm. c) Exactly 64 ppm. d) Greater than 94 ppm.
139
likes695 views
Answer to a math question 6-35 A recent study by an environmental watchdog determined that the amount of contaminants in Minnesota lakes (in parts per million) it has a normal distribution with a mean of 64 ppm and variance of 17.6. Assume that 35 lakes are randomly selected and sampled. Find the probability that the sample average of the amount of contaminants is a) Greater than 72 ppm. b) Between 64 and 72 ppm. c) Exactly 64 ppm. d) Greater than 94 ppm.
Gene
4.5108 Answers
μ = 64
σ = √(17.6/35) = 0.7091242083
a)
Z score =(x - μ)/σ
=(72 - 64)/0.7091242083
=11.28152
P-value from Z-Table:
P(x<72) = 1
P(x>72) = 1 - P(x<72) = 1 - 1
P(x>72) = 0
b)
P(64 < x < 72) = P(x < 72) - 0.5 = 0.5
P(64 < x < 72) = 0.5
c)
The probability of any single value from a continuous distribution is zero
P(64) = 0
d)
Z score =(x - μ)/σ
=(94 - 64)/0.7091242083
=42.30571
P-value from Z-Table:
P(x<94) = 1
P(x>94) = 1 - P(x<94) = 1 - 1
P(x>94) = 0
Frequently asked questions (FAQs)
What is the product of (5+2i) and its conjugate?
+
What is the unit vector in the direction of vector v = 3i - 4j + 2k?
+
What is the value of the sine function at an angle of 30 degrees on the unit circle?
+
New questions in Mathematics