The time it takes glyceraldehyde-3-phosphate dehydrogenase to convert aldehyde to carbolic acid follows a normal distribution with a mean of 19 milliseconds and standard deviation of 4.04 milliseconds. a) What is the probability that it will take glyceraldehyde-3-phosphate dehydrogenase between 15 milliseconds and 20 milliseconds to convert aldehyde to carbolic acid?
b) What is the probability that it will take glyceraldehyde-3-phosphate dehydrogenase more than 20 milliseconds to convert aldehyde to carbolic acid?
c) What is the probability that it will take glyceraldehyde-3-phosphate dehydrogenase less than 15 milliseconds to convert aldehyde to carbolic acid?

For each probability, transform the normal random variable X with mean 19 and s.d. 4.04 to a standard normal random variable Z with mean 0 and s.d. 1, using the rule

Z = (X - 19) / 4.04

(a) Pr[15 ≤ X ≤ 20] = Pr[(15 - 19)/4.04 ≤ (X - 19)/4.04 ≤ (20 - 19)/4.04]

… ≈ Pr[-0.9901 ≤ Z ≤ 0.2475]

… ≈ Pr[Z ≤ 0.2475] - Pr[Z ≤ -0.9901]

(since Z is a continuous random variable)

… ≈ 0.4367

(b) Pr[X > 20] = Pr[(X - 19)/4.04 > (20 - 19)/4.04]

… ≈ Pr[Z > 0.2475]

… ≈ 1 - P[Z ≤ 0.2475]

(taking the complement probability)

… ≈ 0.4023

(c) Pr[X < 15] = 1 - Pr[15 ≤ X ≤ 20] - Pr[X > 20]

(also taking the complement)

… ≈ 0.1611

the central idea is that:

individuals should refuse to cooperate with institutions they believe unjust.

thoreau felt  that governments were more often agents of corruption than justice, even democracies, and that just because the majority feels a certain way does not make it just or correct in absolute terms. he uses the fact that slavery exists in our democracy to support this idea.

he goes on to say that, as a result, people should live true to their own internal laws regarding right and wrong, as a product of reflection and a moral life, rather than following every law that society imposes. 

step-by-step explanation:

answer: there are 453.592 grams in a pound.