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
Notice the picture below
you have the center, the h,k, all you really need is the radius "r"
-4x + 10y = -4
10y = 4x - 4
y = 2/5 x - 2/5 so slope = 2/5
-2 - 2x = 5y
5y = -2x - 2
y = -2/5 x - 2/5 so slope = -2/5
the slope is opposite so the lines are intersecting
answer is A.
which means 26 is 1.5 standard deviations away from the mean.