Answer:
0.07215 = 0.072 to 3 d.p.
Step-by-step explanation:
Central limit theorem explains that the sampling distribution obtained from this distribution will be approximately a normal distribution with
Mean = population mean
μₓ = μ = 9.8 minutes
Standard deviation of the distribution of sample means = σₓ = (σ/√n)
σ = 12 minutes
n = sample size = 30
σₓ = (12/√30) = 2.191
Probability that a random sample of 30 overtime periods would have a (sample) mean length of more than 13 minutes
Required probability = P(x > 13)
Since we've established that this distribution of sample means approximates a normal distribution
We first standardize 13 minutes.
The standardized score for any value is the value minus the mean then divided by the standard deviation.
z = (x - μ)/σ = (13 - 9.8)/2.191 = 1.46
Required probability
P(x > 13) = P(z > 1.46)
We'll use data from the normal probability table for these probabilities
P(x > 13) = P(z > 1.46) = 1 - P(z ≤ 1.46)
= 1 - 0.92785 = 0.07215
Hope this Helps!!!
Answer:
Hyperbola:
Step-by-step explanation:
the given hyperbola has equation:
This is an equation of a hyperbola centered at the origin.
This hyperbola is translated so its center is now at T(4,3)
We expand to get:
Eleven subtract nine is two; eight adding three is eleven (2,11)
Answer:
Step-by-step explanation:
For ellipses, the length of the major axis is represents as:
Major axis = 
where 
is called the semi-major axis.
In this case since the major axis is equal to 10 units:
solving for the semi-major axis :
and also the minor axis of an ellipse is represented as:
Minor axis = 
where 
is called the semi-minor axis.
Since the minor axis has a length of 8 units:
solving for b:
Now we can use the equation for an ellipse centered at the origin (0,0):
and substituting the values for and :
and finall we simplify the expression to get the equation of the ellipse:
