A probability and statistics problem uses z-score. Given mean (mu) = 2,910 psi; std deviation (sigma) = 370.0 psi; value (x) = 5,920 psi, determine the z-score (z).

Start with the thinking

• The governing relation printed in this handbook section is z-score.
• Everything except z is given, so isolate z symbolically first — never rearrange after the numbers are in.
• Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
• Probability and Statistics items reward recognising the unknown before touching a calculator.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$z = (x - \mu) / \sigma$$

2. Step 2 — Rearrange the relation so that z stands alone on the left-hand side.

3. Step 3

   $$List the givens: mean (mu) = 2,910 psi, std deviation (sigma) = 370.0 psi, value (x) = 5,920 psi$$

4. Step 4 — Substitute the given values into the rearranged relation.

5. Step 5 — Evaluate:

   $$z = 8.1351$$

6. Step 6 — Check: returning z = 8.1351 to

   $$z = (x - \mu) / \sigma$$

   reproduces the given quantities, and both sides carry the same units.

Why the other options are there

• 16.2703 — kept a factor of two that cancels in the correct rearrangement.
• 4.0676 — dropped that same factor in the other direction.
• 8.9486 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Probability and Statistics → Cumulative Distribution Functions

A probability and statistics problem uses z-score. Given mean (mu) = 3,140 psi; std deviation (sigma) = 240.0 psi; z-score (z) = -0.8700, determine the value (x) in psi.

Start with the thinking

• The governing relation printed in this handbook section is z-score.
• Everything except x is given, so isolate x symbolically first — never rearrange after the numbers are in.
• Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
• Probability and Statistics items reward recognising the unknown before touching a calculator.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$z = (x - \mu) / \sigma$$

2. Step 2 — Rearrange the relation so that x stands alone on the left-hand side.

3. Step 3

   $$List the givens: mean (mu) = 3,140 psi, std deviation (sigma) = 240.0 psi, z-score (z) = -0.8700$$

4. Step 4 — Substitute the given values into the rearranged relation.

5. Step 5 — Evaluate:

   $$x = 2931\ \text{psi}$$

6. Step 6 — Check: returning x = 2,931 psi to

   $$z = (x - \mu) / \sigma$$

   reproduces the given quantities, and both sides carry the same units.

Why the other options are there

• 5,862 — kept a factor of two that cancels in the correct rearrangement.
• 1,466 — dropped that same factor in the other direction.
• 3,224 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Probability and Statistics → Cumulative Distribution Functions

A probability and statistics problem uses z-score. Given std deviation (sigma) = 530.0 psi; value (x) = 2,150 psi; z-score (z) = 0.1000, determine the mean (mu) in psi.

Start with the thinking

• The governing relation printed in this handbook section is z-score.
• Everything except mu is given, so isolate mu symbolically first — never rearrange after the numbers are in.
• Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
• Probability and Statistics items reward recognising the unknown before touching a calculator.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$z = (x - \mu) / \sigma$$

2. Step 2 — Rearrange the relation so that mu stands alone on the left-hand side.

3. Step 3

   $$List the givens: std deviation (sigma) = 530.0 psi, value (x) = 2,150 psi, z-score (z) = 0.1000$$

4. Step 4 — Substitute the given values into the rearranged relation.

5. Step 5 — Evaluate:

   $$\mu = 2097\ \text{psi}$$

6. Step 6 — Check: returning mu = 2,097 psi to

   $$z = (x - \mu) / \sigma$$

   reproduces the given quantities, and both sides carry the same units.

Why the other options are there

• 4,194 — kept a factor of two that cancels in the correct rearrangement.
• 1,049 — dropped that same factor in the other direction.
• 2,307 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Probability and Statistics → Cumulative Distribution Functions

A probability and statistics problem uses z-score. Given mean (mu) = 5,650 psi; value (x) = 5,540 psi; z-score (z) = 0.1100, determine the std deviation (sigma) in psi.

Start with the thinking

• The governing relation printed in this handbook section is z-score.
• Everything except sigma is given, so isolate sigma symbolically first — never rearrange after the numbers are in.
• Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
• Probability and Statistics items reward recognising the unknown before touching a calculator.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$z = (x - \mu) / \sigma$$

2. Step 2 — Rearrange the relation so that sigma stands alone on the left-hand side.

3. Step 3

   $$List the givens: mean (mu) = 5,650 psi, value (x) = 5,540 psi, z-score (z) = 0.1100$$

4. Step 4 — Substitute the given values into the rearranged relation.

5. Step 5 — Evaluate:

   $$\sigma = -1000\ \text{psi}$$

6. Step 6 — Check: returning sigma = -1,000 psi to

   $$z = (x - \mu) / \sigma$$

   reproduces the given quantities, and both sides carry the same units.

Why the other options are there

• -2,000 — kept a factor of two that cancels in the correct rearrangement.
• -500.0 — dropped that same factor in the other direction.
• -1,100 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Probability and Statistics → Cumulative Distribution Functions

A probability and statistics problem uses z-score. Given mean (mu) = 3,540 psi; std deviation (sigma) = 430.0 psi; value (x) = 3,940 psi, determine the z-score (z).

Start with the thinking

• The governing relation printed in this handbook section is z-score.
• Everything except z is given, so isolate z symbolically first — never rearrange after the numbers are in.
• Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
• Probability and Statistics items reward recognising the unknown before touching a calculator.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$z = (x - \mu) / \sigma$$

2. Step 2 — Rearrange the relation so that z stands alone on the left-hand side.

3. Step 3

   $$List the givens: mean (mu) = 3,540 psi, std deviation (sigma) = 430.0 psi, value (x) = 3,940 psi$$

4. Step 4 — Substitute the given values into the rearranged relation.

5. Step 5 — Evaluate:

   $$z = 0.9302$$

6. Step 6 — Check: returning z = 0.9302 to

   $$z = (x - \mu) / \sigma$$

   reproduces the given quantities, and both sides carry the same units.

Why the other options are there

• 1.8605 — kept a factor of two that cancels in the correct rearrangement.
• 0.4651 — dropped that same factor in the other direction.
• 1.0233 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Probability and Statistics → Cumulative Distribution Functions

A probability and statistics problem uses z-score. Given mean (mu) = 5,900 psi; std deviation (sigma) = 190.0 psi; z-score (z) = 0.0200, determine the value (x) in psi.

Start with the thinking

• The governing relation printed in this handbook section is z-score.
• Everything except x is given, so isolate x symbolically first — never rearrange after the numbers are in.
• Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
• Probability and Statistics items reward recognising the unknown before touching a calculator.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$z = (x - \mu) / \sigma$$

2. Step 2 — Rearrange the relation so that x stands alone on the left-hand side.

3. Step 3

   $$List the givens: mean (mu) = 5,900 psi, std deviation (sigma) = 190.0 psi, z-score (z) = 0.0200$$

4. Step 4 — Substitute the given values into the rearranged relation.

5. Step 5 — Evaluate:

   $$x = 5904\ \text{psi}$$

6. Step 6 — Check: returning x = 5,904 psi to

   $$z = (x - \mu) / \sigma$$

   reproduces the given quantities, and both sides carry the same units.

Why the other options are there

• 11,808 — kept a factor of two that cancels in the correct rearrangement.
• 2,952 — dropped that same factor in the other direction.
• 6,494 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Probability and Statistics → Cumulative Distribution Functions

A probability and statistics problem uses z-score. Given std deviation (sigma) = 370.0 psi; value (x) = 4,030 psi; z-score (z) = 2.5100, determine the mean (mu) in psi.

Start with the thinking

• The governing relation printed in this handbook section is z-score.
• Everything except mu is given, so isolate mu symbolically first — never rearrange after the numbers are in.
• Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
• Probability and Statistics items reward recognising the unknown before touching a calculator.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$z = (x - \mu) / \sigma$$

2. Step 2 — Rearrange the relation so that mu stands alone on the left-hand side.

3. Step 3

   $$List the givens: std deviation (sigma) = 370.0 psi, value (x) = 4,030 psi, z-score (z) = 2.5100$$

4. Step 4 — Substitute the given values into the rearranged relation.

5. Step 5 — Evaluate:

   $$\mu = 3101\ \text{psi}$$

6. Step 6 — Check: returning mu = 3,101 psi to

   $$z = (x - \mu) / \sigma$$

   reproduces the given quantities, and both sides carry the same units.

Why the other options are there

• 6,203 — kept a factor of two that cancels in the correct rearrangement.
• 1,551 — dropped that same factor in the other direction.
• 3,411 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Probability and Statistics → Cumulative Distribution Functions

A probability and statistics problem uses z-score. Given mean (mu) = 5,730 psi; value (x) = 3,440 psi; z-score (z) = 2.5200, determine the std deviation (sigma) in psi.

Start with the thinking

• The governing relation printed in this handbook section is z-score.
• Everything except sigma is given, so isolate sigma symbolically first — never rearrange after the numbers are in.
• Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
• Probability and Statistics items reward recognising the unknown before touching a calculator.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$z = (x - \mu) / \sigma$$

2. Step 2 — Rearrange the relation so that sigma stands alone on the left-hand side.

3. Step 3

   $$List the givens: mean (mu) = 5,730 psi, value (x) = 3,440 psi, z-score (z) = 2.5200$$

4. Step 4 — Substitute the given values into the rearranged relation.

5. Step 5 — Evaluate:

   $$\sigma = -908.7\ \text{psi}$$

6. Step 6 — Check: returning sigma = -908.7 psi to

   $$z = (x - \mu) / \sigma$$

   reproduces the given quantities, and both sides carry the same units.

Why the other options are there

• -1,817 — kept a factor of two that cancels in the correct rearrangement.
• -454.4 — dropped that same factor in the other direction.
• -999.6 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Probability and Statistics → Cumulative Distribution Functions

A probability and statistics problem uses z-score. Given mean (mu) = 4,550 psi; std deviation (sigma) = 450.0 psi; value (x) = 6,190 psi, determine the z-score (z).

Start with the thinking

• The governing relation printed in this handbook section is z-score.
• Everything except z is given, so isolate z symbolically first — never rearrange after the numbers are in.
• Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
• Probability and Statistics items reward recognising the unknown before touching a calculator.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$z = (x - \mu) / \sigma$$

2. Step 2 — Rearrange the relation so that z stands alone on the left-hand side.

3. Step 3

   $$List the givens: mean (mu) = 4,550 psi, std deviation (sigma) = 450.0 psi, value (x) = 6,190 psi$$

4. Step 4 — Substitute the given values into the rearranged relation.

5. Step 5 — Evaluate:

   $$z = 3.6444$$

6. Step 6 — Check: returning z = 3.6444 to

   $$z = (x - \mu) / \sigma$$

   reproduces the given quantities, and both sides carry the same units.

Why the other options are there

• 7.2889 — kept a factor of two that cancels in the correct rearrangement.
• 1.8222 — dropped that same factor in the other direction.
• 4.0089 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Probability and Statistics → Cumulative Distribution Functions

A probability and statistics problem uses z-score. Given mean (mu) = 2,790 psi; std deviation (sigma) = 400.0 psi; z-score (z) = 2.7400, determine the value (x) in psi.

Start with the thinking

• The governing relation printed in this handbook section is z-score.
• Everything except x is given, so isolate x symbolically first — never rearrange after the numbers are in.
• Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
• Probability and Statistics items reward recognising the unknown before touching a calculator.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$z = (x - \mu) / \sigma$$

2. Step 2 — Rearrange the relation so that x stands alone on the left-hand side.

3. Step 3

   $$List the givens: mean (mu) = 2,790 psi, std deviation (sigma) = 400.0 psi, z-score (z) = 2.7400$$

4. Step 4 — Substitute the given values into the rearranged relation.

5. Step 5 — Evaluate:

   $$x = 3886\ \text{psi}$$

6. Step 6 — Check: returning x = 3,886 psi to

   $$z = (x - \mu) / \sigma$$

   reproduces the given quantities, and both sides carry the same units.

Why the other options are there

• 7,772 — kept a factor of two that cancels in the correct rearrangement.
• 1,943 — dropped that same factor in the other direction.
• 4,275 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Probability and Statistics → Cumulative Distribution Functions