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 standard deviation of a sample set of numbers: 5, 7, 9, 11?
+
What is the length of the side opposite an angle of 45° with a hypotenuse of 10 using SOH CAH TOA?
+
Math question: What is the limit as x approaches 2 of (3x^2 - 16x + 12)/(x - 2)?
+
New questions in Mathematics