Concrete strength has a known standard deviation of 185.0 psi. How many cylinders must be tested so that the mean is estimated within ±11 psi at a z of 2.576?

Start with the thinking

• Sample size scales with the square of the ratio σ/E — halving the margin quadruples the testing.
• Always round the computed sample size up to the next whole specimen.

Step-by-step solution

1. Formula

   $$n = (z \sigma / E)^{2}$$

2. Substituting

   $$n = (2.576 \times 185.0 / 11)^{2}$$

3. Inside the bracket — 43.3236

4. Evaluate

   $$n = 1,877 \to 1877 specimens$$

Why the other options are there

• 44 (forgot to square)
• 939 (halved the requirement)

Reference: FE Reference Handbook — Probability and Statistics → Sample Size

Concrete strength has a known standard deviation of 210.0 psi. How many cylinders must be tested so that the mean is estimated within ±42 psi at a z of 1.645?

Start with the thinking

• Sample size scales with the square of the ratio σ/E — halving the margin quadruples the testing.
• Always round the computed sample size up to the next whole specimen.

Step-by-step solution

1. Formula

   $$n = (z \sigma / E)^{2}$$

2. Substituting

   $$n = (1.645 \times 210.0 / 42)^{2}$$

3. Inside the bracket — 8.2250

4. Evaluate

   $$n = 67.65 \to 68 specimens$$

Why the other options are there

• 9 (forgot to square)
• 34 (halved the requirement)

Reference: FE Reference Handbook — Probability and Statistics → Sample Size

Concrete strength has a known standard deviation of 165.0 psi. How many cylinders must be tested so that the mean is estimated within ±21 psi at a z of 1.645?

Start with the thinking

• Sample size scales with the square of the ratio σ/E — halving the margin quadruples the testing.
• Always round the computed sample size up to the next whole specimen.

Step-by-step solution

1. Formula

   $$n = (z \sigma / E)^{2}$$

2. Substituting

   $$n = (1.645 \times 165.0 / 21)^{2}$$

3. Inside the bracket — 12.9250

4. Evaluate

   $$n = 167.1 \to 168 specimens$$

Why the other options are there

• 13 (forgot to square)
• 84 (halved the requirement)

Reference: FE Reference Handbook — Probability and Statistics → Sample Size

Concrete strength has a known standard deviation of 185.0 psi. How many cylinders must be tested so that the mean is estimated within ±46 psi at a z of 1.96?

Start with the thinking

• Sample size scales with the square of the ratio σ/E — halving the margin quadruples the testing.
• Always round the computed sample size up to the next whole specimen.

Step-by-step solution

1. Formula

   $$n = (z \sigma / E)^{2}$$

2. Substituting

   $$n = (1.96 \times 185.0 / 46)^{2}$$

3. Inside the bracket — 7.8826

4. Evaluate

   $$n = 62.14 \to 63 specimens$$

Why the other options are there

• 8 (forgot to square)
• 32 (halved the requirement)

Reference: FE Reference Handbook — Probability and Statistics → Sample Size

Concrete strength has a known standard deviation of 270.0 psi. How many cylinders must be tested so that the mean is estimated within ±49 psi at a z of 2.576?

Start with the thinking

• Sample size scales with the square of the ratio σ/E — halving the margin quadruples the testing.
• Always round the computed sample size up to the next whole specimen.

Step-by-step solution

1. Formula

   $$n = (z \sigma / E)^{2}$$

2. Substituting

   $$n = (2.576 \times 270.0 / 49)^{2}$$

3. Inside the bracket — 14.1943

4. Evaluate

   $$n = 201.5 \to 202 specimens$$

Why the other options are there

• 15 (forgot to square)
• 101 (halved the requirement)

Reference: FE Reference Handbook — Probability and Statistics → Sample Size

Concrete strength has a known standard deviation of 305.0 psi. How many cylinders must be tested so that the mean is estimated within ±19 psi at a z of 2.576?

Start with the thinking

• Sample size scales with the square of the ratio σ/E — halving the margin quadruples the testing.
• Always round the computed sample size up to the next whole specimen.

Step-by-step solution

1. Formula

   $$n = (z \sigma / E)^{2}$$

2. Substituting

   $$n = (2.576 \times 305.0 / 19)^{2}$$

3. Inside the bracket — 41.3516

4. Evaluate

   $$n = 1,710 \to 1710 specimens$$

Why the other options are there

• 42 (forgot to square)
• 855 (halved the requirement)

Reference: FE Reference Handbook — Probability and Statistics → Sample Size

Concrete strength has a known standard deviation of 385.0 psi. How many cylinders must be tested so that the mean is estimated within ±46 psi at a z of 1.96?

Start with the thinking

• Sample size scales with the square of the ratio σ/E — halving the margin quadruples the testing.
• Always round the computed sample size up to the next whole specimen.

Step-by-step solution

1. Formula

   $$n = (z \sigma / E)^{2}$$

2. Substituting

   $$n = (1.96 \times 385.0 / 46)^{2}$$

3. Inside the bracket — 16.4043

4. Evaluate

   $$n = 269.1 \to 270 specimens$$

Why the other options are there

• 17 (forgot to square)
• 135 (halved the requirement)

Reference: FE Reference Handbook — Probability and Statistics → Sample Size

Concrete strength has a known standard deviation of 295.0 psi. How many cylinders must be tested so that the mean is estimated within ±49 psi at a z of 1.645?

Start with the thinking

• Sample size scales with the square of the ratio σ/E — halving the margin quadruples the testing.
• Always round the computed sample size up to the next whole specimen.

Step-by-step solution

1. Formula

   $$n = (z \sigma / E)^{2}$$

2. Substituting

   $$n = (1.645 \times 295.0 / 49)^{2}$$

3. Inside the bracket — 9.9036

4. Evaluate

   $$n = 98.08 \to 99 specimens$$

Why the other options are there

• 10 (forgot to square)
• 50 (halved the requirement)

Reference: FE Reference Handbook — Probability and Statistics → Sample Size

Concrete strength has a known standard deviation of 295.0 psi. How many cylinders must be tested so that the mean is estimated within ±41 psi at a z of 1.645?

Start with the thinking

• Sample size scales with the square of the ratio σ/E — halving the margin quadruples the testing.
• Always round the computed sample size up to the next whole specimen.

Step-by-step solution

1. Formula

   $$n = (z \sigma / E)^{2}$$

2. Substituting

   $$n = (1.645 \times 295.0 / 41)^{2}$$

3. Inside the bracket — 11.8360

4. Evaluate

   $$n = 140.1 \to 141 specimens$$

Why the other options are there

• 12 (forgot to square)
• 71 (halved the requirement)

Reference: FE Reference Handbook — Probability and Statistics → Sample Size

Concrete strength has a known standard deviation of 335.0 psi. How many cylinders must be tested so that the mean is estimated within ±21 psi at a z of 1.96?

Start with the thinking

• Sample size scales with the square of the ratio σ/E — halving the margin quadruples the testing.
• Always round the computed sample size up to the next whole specimen.

Step-by-step solution

1. Formula

   $$n = (z \sigma / E)^{2}$$

2. Substituting

   $$n = (1.96 \times 335.0 / 21)^{2}$$

3. Inside the bracket — 31.2667

4. Evaluate

   $$n = 977.6 \to 978 specimens$$

Why the other options are there

• 32 (forgot to square)
• 489 (halved the requirement)

Reference: FE Reference Handbook — Probability and Statistics → Sample Size