How do I solve this problem step by step?
1 answer:
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Answer:
a) 0.1587
b) 0.0475
c) 0.7938
Step-by-step explanation:
Let's start defining our random variable.
X : ''Thickness (in mm) of ancient prehistoric Native American pot shards discovered in a Hopi village''
X is modeled as a normal random variable.
X ~ N(μ,σ)
Where μ is the mean and σ is the standard deviation.
To calculate all the probabilities, we are going to normalize the random variable X.
We are going to call to the standard normal distribution ''Z''.
[(X - μ) / σ] ≅ Z
We normalize by subtracting the mean to X and then dividing by standard deviation.
We can find the values of probabilities for Z in a standard normal distribution table.
We are going to call Φ(A) to the normal standard cumulative distribution evaluated in a value ''A''
a)
Φ(-1) = 0.1587
b)
1 - Φ(1.666) = 1 - 0.9525 = 0.0475
c)
Φ(1.666) - Φ(-1) = 0.9525 - 0.1587 = 0.7938
Answer:
24.39mL of the solution would be given per hour.
Step-by-step explanation:
This problem can be solved by direct rule of three, in which there are a direct relationship between the measures, which means that the rule of three is a cross multiplication.
The first step to solve this problem is to see how many mg of the solution is administered per hour.
Each minute, 200 ug are administered. 1mg has 1000ug, so
1mg - 1000 ug
xmg - 200 ug
In each minute, 0.2 mg are administered. Each hour has 60 minutes. How many mg are administered in 60 minutes?
1 minute - 0.2 mg
60 minutes - x mg
In an hour, 12 mg of the drug is administered. In 250 mL, there is 123 mg of the drug. How many ml are there in 12 mg of the drug.
123mg - 250mL
12 mg - xmL
mL
24.39mL of the solution would be given per hour.