3 When measuring the thickness of wood, the reading on the caliper is 49 mm. The standard deviation of the reading from 0.5 mm.The error from the wear of the caliper jaws is Delta S=-0.8mm The confidence limits for the true value of the thickness with a probability of P-0.9973 (1-3) will be Select one answer C a. 47.7umshs50,314M (P 0.9973) b 46.7mushs49.7mm(P0.9973) c. 47,5uushs50,5mu (tp 3) A d 48,3unshleqslant 51,3uM(P0,9973)

To find the confidence limits for the true value of the thickness with a probability of $P = 0.9973$, we need to consider the standard deviation and the error from the wear of the caliper jaws.<br /><br />Given:<br />- Reading on the caliper: 49 mm<br />- Standard deviation: 0.5 mm<br />- Error from the wear of the caliper jaws: $\Delta S = -0.8$ mm<br />- Probability: $P = 0.9973$<br /><br />The confidence limits can be calculated using the formula:<br /><br />\[ \text{Confidence Limits} = \text{Reading} \pm (z \times \text{Standard Deviation}) \]<br /><br />Where $z$ is the z-score corresponding to the given probability.<br /><br />For $P = 0.9973$, the z-score is approximately 2.81.<br /><br />Now, let's calculate the confidence limits:<br /><br />\[ \text{Lower Limit} = 49 - (2.81 \times 0.5) = 49 - 1.405 = 47.595 \]<br />\[ \text{Upper Limit} = 49 + (2.81 \times 0.5) = 49 + 1.405 = 50.405 \]<br /><br />Therefore, the confidence limits for the true value of the thickness with a probability of $P = 0.9973$ are approximately 47.6 mm to 50.4 mm.<br /><br />So, the correct answer is:<br />b. $46.7mm \leqslant 49.7mm (P0.9973)$