---
title: "Fiducial limits for mean, sample of 900"
subject: "Probability and Statistics"
chapter: 6
key: "semester_5/probability_and_statistics:fiducial-limits-sample-900"
source: https://www.bctengineer.com/q/semester_5/probability_and_statistics/fiducial-limits-sample-900
site: BCT Engineering
---

# Fiducial limits for mean, sample of 900

Probability and Statistics · Chapter 6: Inference concerning mean

- Asked in: 2068 Chaitra, 5 marks
- Video: [A sample of 900 members has a mean 3.4 cm and standard deviation 2.61 cm.|Large sample - 1 || MA3251](https://www.youtube.com/watch?v=Elm3XTZ35kE) — Maths Tutor Sherly
- Answer checked by Claude Sonnet 5.5 on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_5/probability_and_statistics/fiducial-limits-sample-900
- Whole chapter: https://www.bctengineer.com/md/semester_5/probability_and_statistics/chapter-6

## Question

The sample of 900 members has a mean of 3.4 cms and standard deviation 2.61 cms. If the population is normal and its mean is unknown, find 95% and 98% fiducial limits of true mean.

## Short answer

Large sample, use z-interval with s: SE=0.087 cm. 95% limits: 3.4 ± 1.96*0.087 = (3.23, 3.57) cm. 98% limits: 3.4 ± 2.326*0.087 = (3.20, 3.60) cm.

## Answer

Fiducial (confidence) limits for a population mean are x̄ ± z·s/√n. The sample is large (n = 900), so the normal distribution is used and s replaces the unknown σ.

```text
n = 900, x̄ = 3.4 cm, s = 2.61 cm
SE = s/√n = 2.61/√900 = 2.61/30 = 0.0870
```

#### 95% limits

z = 1.960

```text
margin = 1.960 × 0.0870 = 0.1705
limits = 3.4 ± 0.1705 = (3.229, 3.571)
```

#### 98% limits

z = 2.326

```text
margin = 2.326 × 0.0870 = 0.2024
limits = 3.4 ± 0.2024 = (3.198, 3.602)
```

**Answer: 95% fiducial limits: 3.23 cm to 3.57 cm; 98% fiducial limits: 3.20 cm to 3.60 cm.** The higher the confidence level, the wider the interval.

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. Why z?
   A. skewed
   B. n small
   C. sigma known exactly
   D. n = 900 large
   Answer: D. Large sample so normal critical values and s for sigma. (Key point: Distribution)

2. What is SE?
   A. 2.61/900
   B. 2.61/30 = 0.087
   C. 2.61 x 30
   D. 2.61^2/900
   Answer: B. SE = 0.087. (Key point: Standard error)

3. Which z for 95% and 98%?
   A. 2.576 and 2.326
   B. 1.960 and 2.326
   C. 1.96 and 2.576
   D. 1.645 and 1.96
   Answer: B. 98% two-sided uses 2.326. (Key point: Critical values)

4. What happens with higher confidence?
   A. Interval gets wider
   B. Unchanged
   C. Narrower
   D. Shifts
   Answer: A. 98% limits (3.198, 3.602) are wider than 95% (3.229, 3.571). (Key point: Width)

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