Answer:
The likelihood that Albert's sample of 64 will have a mean waiting time between 13.5 and 16.5 minutes is 0.9973.
Step-by-step explanation:
Prior concepts
A normal distribution is characterized as a "probability distribution that is symmetric around the mean, indicating that data close to the mean are more frequent than those further away".
The Z-score refers to "a statistical measurement that reflects the relationship of a value to the mean of a group, measured in standard deviations".
Let X denote the random variable of interest, and we identify its distribution:
Also, let 
signify the sample mean, whose distribution is:
In this case, 
Solution to the problem
We seek this probability
Applying the Z-score formula to the probability results in:
To determine these probabilities, we can refer to normal distribution tables, use Excel, or a calculator.
The likelihood that Albert's sample of 64 will have a mean waiting time between 13.5 and 16.5 minutes is 0.9973.
Answer:
Please refer below.
Step-by-step explanation:
Given points:
- S(-3,6),T(0,7),U(1,4),and V(-5,2)
Translation rule:
New coordinates after applying the rule:
- S'(4, -3), T'(7, -2), U'(8, -5), V'(2, -7)
For the graph, see attached.
The trapezoid highlighted in blue is STUV while the red trapezoid is S'T'U'V'
Given that we only have the first measurement accurate to three significant figures, we can simplify the rest to 10, estimating the total at 2620.
9514 1404 393
Answer:
∛(2500π)√37 m² ≈ 120.911 m²
Step-by-step explanation:
If the height of the cone is three times the diameter, that means it is six times the radius. Hence, the volume is computed as...
V = 1/3πr²h
V = 1/3πr²(6r) = 2πr³
To find the radius for a volume of 100 m³, solve...
100 m³ = 2πr³
r = ∛(50/π) m
To calculate the lateral area, the slant height must be found using the Pythagorean theorem:
s² = r² +(6r)² = 37r²
s = r√37
Thus, the lateral area is calculated as...
LA = πrs
LA = π(∛(50/π) m)(∛(50/π) m)√37
LA = ∛(2500π)√37 m² ≈ 120.911 m²
