Respuesta :
Answer:
a) 0.09012
b) 0.50116
c) The threshold such that it is 3.25 standard deviations above the mean is 12.41ppm.
And 0.99865 of the CO data range will fall within the range of the threshold.
Only 0.00135 will exceed the threshold.
Step-by-step explanation:
Mean, xbar = 6.23 ppm
Standard deviation = √variance = √4.26 = 2.06ppm
a) To find the probability that the CO level exceeds 9 ppm
We need to standardize 9ppm
z = (x - xbar)/σ = (9 - 6.23)/2.06 = 1.34
P(x > 9) = P(x > 1.34)
We'll use data from the normal probability table for these probabilities
P(x > 9) = P(z > 1.34) = 1 - P(z ≤ 1.34) = 1 - 0.90988 = 0.09012
b) To find the probability that the CO level is between 5.5 ppm and 8.5 ppm
We need to standardize 5.5ppm and 8.5ppm
z = (x - xbar)/σ = (5.5 - 6.23)/2.06 = - 0.35
z = (x - xbar)/σ = (8.5 - 6.23)/2.06 = 1.10
P(5.5 < x < 8.5) = P(-0.35 < z < 1.10)
We'll use data from the normal probability table for these probabilities
P(5.5 < x < 8.5) = P(-0.35 < z < 1.10) = P(z ≤ 1.10) - P(z ≤ -0.35) = 0.86433 - 0.36317 = 0.50116
c) An alarm is to be activated if the CO levels exceed a certain threshold. Specify the threshold such that it is 3.25 standard deviations above the mean.
x = 3σ + xbar = 3(2.06) + 6.23 = 12.41ppm
The amount of CO within the range of the threshold
P(z < 3) = 1 - P(z ≥ 3) = 1 - P(z ≤ -3) = 1 - 0.00135 = 0.99865
Hope this Helps!!!
