What is the population standard deviation

Assignment Help Engineering Mathematics

Reference no: EM134009726

Engineering & Statistics Questions

Question 1. Area Conversion

How many cm² is equal to 0.53m²? For similar Applied Mathematics problems and unit conversion concepts, practice additional numerical exercises.

Question 2. Current Conversion

0.174A is equal to ____ mA

Question 3. Mean, Median and Mode

A delivery of 27 cars to a dealership are found to have the following number of defects:

[6, 7, 3, 8, 0, 7, 1, 3, 0, 3, 8, 5, 2, 0, 9, 1, 6, 3, 2, 3, 1, 3, 7, 4, 0, 4, 5]

a) What is the mean number of defects?
b) What is the median number of defects?
c) What is the mode?

These concepts are commonly covered in Statistics and Mean Deviation assignments.

Question 4. Cumulative Frequency & Percentage

A sample of 50 plastic toggle levers with a nominal thickness of 1.85mm were measured and recorded the following actual thickness measurements in mm.

1.83 1.90 1.94 1.85 2.06 2.18 1.93 1.96 1.87 2.13
1.55 1.88 1.94 1.91 1.91 1.91 1.73 1.89 1.84 2.03
1.91 1.97 1.79 1.96 1.67 2.07 1.68 1.85 1.83 2.11
1.98 1.77 2.01 2.07 2.08 1.49 1.96 1.96 1.69 1.83
1.66 1.74 2.12 1.96 1.87 1.96 1.75 1.71 1.84 1.96

By drawing a cumulative frequency chart or otherwise, calculate percentage of levers that don’t have less than the nominal thickness.

For related data analysis techniques, refer to Statistics resources and probability-based problem solving.

Question 5. Standard Deviation of Resistors

The measured resistance of a sample 10 resistors from a box of 600 is as below. All values are in Ohms (Ω).

80.62 81.57 81.50 81.54 80.80 81.43 79.13 79.83 83.90 81.20

a) What is the sample standard deviation?
b) What is the population standard deviation?

Additional help on deviation and probability calculations is available in Probability topics.

Question 6. Grouped Frequency Distribution

Measurements of the mass of a large sample of steel reinforcement rods produced the following table:

Class (kg)	Frequency
3.005–3.035	4
3.035–3.065	8
3.065–3.095	14
3.095–3.125	23
3.125–3.155	28
3.155–3.185	37
3.185–3.215	39
3.215–3.245	34
3.245–3.275	27
3.275–3.305	20

a) Calculate the mean to three decimal places.
b) Calculate the standard deviation. Round your answer to 3 decimal places.

Question 7. Coplanar Force System

For the co-planar force system shown below, determine by calculation, the resultant force in magnitude and direction.

220N at 140°
180N horizontally right
130N vertically downward
160N at 50°

a) Find the magnitude.

In x direction ___ N
In y direction ___ N
Total ___ N

b) Find the direction in the range: 0° ≤ direction < 360°

Question 8. Loaded Framework Joint

A joint which is part of a loaded framework is shown below. The joint carries a vertically downward load of 19kN as shown and the horizontal force in OP is 6kN acting towards O. Concepts related to mechanics are commonly applied in analysing framework joints and force systems.

a) Find the force in member OR.

b) Find the force in member OQ.

Question 9. Beam Reactions

A uniform beam of length 5m is simply supported at A and B. It carries a vertically downward load of 30kN and is to carry a further 30kN load such that the upward reactions at each support are equal.

Determine the position of the 30kN load from A.

Question 10. Fluid Pressure

Calculate the pressure exerted at the base of a 3.8m high column of citric acid with a density of 1665 kg·m?³. Topics involving fluid mechanics frequently require pressure and density calculations.

Use g = 9.81 m·s?².

Give your answer in bar to 2 decimal places.

Question 11. Volumetric Flow Rate

A fluid flows along a pipe of radius 79mm with an average velocity of 16 m/s.

Take π as 3.142.

Calculate the volumetric rate of flow (q?) in m³/s to 3 significant figures.

Question 12. Air Flow Through Heated Pipe

Air with a density of 1.26 kg·m?³ is pumped into a pipe of radius 85cm at a rate of 6 m³/s.

It then passes through a heater and emerges with a density of 1.12 kg·m?³. At the exit point, the pipe diameter is 90cm.

Using π = 3.142 and 2 decimal places:

a) Determine the velocity of the air entering the pipe.

b) Determine the mass flowrate.

c) Determine the velocity of the air leaving the heater.

Fluid Mechanics & Heat Transfer Questions

Question 13. Crude Oil Pipe Flow System

Crude oil of density 862 kg·m?³ flows steadily along the pipe system shown below. Additional practice in fluid mechanics can help in solving pipe flow and volumetric flow rate problems.

The volumetric flow rate of the crude oil is 490 litres per second.

Take π = 3.142 and assume that all pipes run full.

Determine the following to 2 decimal places:

a) The specific volume of the crude oil

vs = ____ × 10?³ m³·kg?¹

b) The mass flow rate at A

qmA = ____ kg·s?¹

c) The velocity of flow at A

velA = ____ m·s?¹

d) The volumetric flow rate at C

volC = ____ m³·s?¹

e) The volumetric flow rate at B

volB = ____ m³·s?¹

f) The velocity of flow at B

velB = ____ m·s?¹

Question 14. Heat Transfer Through a Wall

Given that the equation for the rate of heat transfer (?) through a solid by conduction is:

where:

k = thermal conductivity of the material (W·K?¹·m?¹)
A = surface area (m²)
∇T = temperature gradient (K·m?¹)

Calculate the heat that will pass through a wall measuring:

4.5m × 7.5m
Thickness = 0.3m
Thermal conductivity = 1.3 W·m?¹·K?¹
Inside temperature = 444K (171°C)
Outside temperature = 305K (32°C)

Reference no: EM134009726

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