The monthly sales of a plywood shop are normally distributed with a standard deviation of Rs. 900. A statistical study of sales in the last nine months has found a confidence interval for the mean monthly sales with extremes Rs. 4663 and Rs. 5839. What were the average sales over the nine-month period?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → Rs. 5251
A confidence interval for the mean is centred at the sample mean:
\( \displaystyle \text{interval}=\bar{x}\pm\text{margin of error} \)
So the sample mean is the midpoint of the two extremes:
\( \displaystyle \bar{x}=\frac{4663+5839}{2} \)
\( \displaystyle =\frac{10502}{2}=5251 \)
The average sales over the nine months were Rs. 5251. (The standard deviation and the sample size are needed only to find the margin of error, 5839 − 5251 = Rs. 588.)