A supplier sends steel plates in a huge quantity to a contractor. The first batch was exhaustively examined for thickness and gave a standard deviation of 1·80. The contractor feels that the knowledge of mean within a range of 0·5 to its true value for a probability of 95% would be satisfactory. What is the size of sample ?
- A40 numbers
- B30 numbers
- C60 numbers
- D50 numbersCorrect
Solution
Concept
Sample size for a given confidence interval
Formula
n = (z σ / E)²
Step-by-step solution
1. z = 1.96 for 95%, σ = 1.80, E = 0.5. 2. n = (1.96 × 1.80 / 0.5)² = (7.056)² = 49.8 ≈ 50.
Explanation
The sample must be large enough so that the 95% confidence interval for the mean is not wider than ±0.5.
Why the other options are wrong
30, 40 and 60 give half-widths of 0.64, 0.56 and 0.46.
Shortcut
n = (zσ/E)².
Common mistake
Using z = 2 gives 52 (still nearest to 50).
Correct answer: D) 50 numbers