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The Buffon’s needle problem is a random experiment leading to estimate of the number π by ”randomly” throwing a
needle onto a plane partitioned by parallel lines. Indeed, in the independently repetitions of the experiment, based on
the number of times where the needle will cross a line, one can construct an estimator of π. The aim of this note is to
obtain a better estimator (in some sense) by considering a model where the plane is partitioned by rectangles. We show
that both estimators are asymptotically normal and unbiased; and also the confidence intervals are obtained for π. We
calculate the asymptotic relative efficiency of the estimators and show that the estimator based on the rectangles is more
efficient. The data of a real experiment is provided.

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In this article, based on a random sample from a normal distribution with unknown parameters, we obtain the shortest confidence interval for the standard deviation parameter using the sample standard deviation. We show that this confidence interval cannot be obtained by taking the square root of the endpoints of the shortest confidence interval for the variance given by Tate and Klett.  A table is provided to calculate the confidence interval for several sample sizes and three common confidence coefficients. Also, the power performance of the tests made based on the mentioned confidence intervals is considered.