Ms. Ramirez wrote a test. Part A had true/false questions, each worth 4 points. Part B had multiple choice questions, each worth
2 answers:
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Answer:
5.48% of the people in line waited for more than 28 minutes
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean and standard deviation
, the z-score of a measure X is given by:
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Mean waiting time of 20 minutes with a standard deviation of 5 minutes.
This means that
What percentage of the people in line waited for more than 28 minutes?
The proportion is 1 subtracted by the p-value of Z when X = 28. So
has a p-value of 0.9452.
1 - 0.9452 = 0.0548.
As a percentage:
0.0548*100% = 5.48%
5.48% of the people in line waited for more than 28 minutes
Answer:
1. The amount of ice needed for the sculpture is 18 m³
2. The amount of fabric needed to manufacture the umbrella is 0.757 m²
3. The height of the cone is 37.5 cm
4. The largest possible storage area which is obtained by attaching the storage area to the back of the building is 87.11 m²
Step-by-step explanation:
1. The volume, V, of a rectangular pyramid =
Where:
B = Base area = Length, L × Width, W
h = Height of the pyramid = 3.6 m
L = 5 m
W = 3 m
The volume = 1/3 × 5 × 3 × 3.6 = 18 m³
The amount of ice needed for the sculpture is 18 m³
2) The surface area of a cone = π·r·s
s = Slant height
r = Radius of the cone's base = 0.4 m
h = The height of the cone = 0.45m
s = √(0.4² + 0.45²) = (√145)/20
The surface area of the cone = π × 0.4 × (√145)/20 = 0.757 m²
The amount of fabric needed to manufacture the umbrella is 0.757 m²
3) The volume, V of the cone = 150 cm³
The base area, , of the cone = 12 cm²
The height of the cone = h
We note that the volume of a cone =
Therefore;
4·h = 150
h = 150/4 = 37.5 cm
The height of the cone = 37.5 cm
4) The storage area at the back corner with four sides = 100 m²
The storage area at the back of the building with three sides = 98 m²
Given that the available riling = 28 m, we have;
For maximum area the four sides should be equal, hence dimension of each side = 28/4 = 7
The area of storage space that can be fenced on four sides at the back corner = 7 × 7 = 49 m²
At the back of the building only three sides need fencing, we therefore have;
The side length = 28/3 =
The area fenced = = 87.11 m²
Therefore, the largest possible storage area, 87.11 m², is obtained by attaching the storage area to the back of the building.