2.- Si las estaturas de un conjunto de personas adultas se distribuyen aproximadamente conforme a una curva normal y si su promedio aritmético y desviación estándar son respectivamente; 1.62 y 0.03 metros. Encuentre: (valor \( 10 \% \) ) A) La probabilidad de que un clerto número de personas tengan una estatura entre 1.64 y 1.67 . B) La probabilidad de que un cierto número de personas tengan una estatura entre la media y \( x=1.66 \).

A water bottling facility has a mean bottling rate of 33.5 thousand bottles per hour with a standard deviation of 1.92 thousand bottles. A nearby cola bottling facility has a mean bottling rate of 26.2 thousand bottles per hour with a standard deviation of 1.42 thousand bottles. One Wednesday from noon to \( 1: 00 \) p.m., the water bottling facility bottled 36.8 thousand bottles of water, and the cola bottling facility bottled 28.4 thousand bottles of cola. Which facility increased their efficiency more during that hour? Answer

Scores on a test have a mean of 78 and a standard deviation of 13 . Tom has a score of 66 . Convert Tom's score to a \( z \)-score, rounded to the nearest hundredth.

Construct a box plot from the given data. Diameters of Cans in an Assembly Line: \( 5.8,5.7,5.2,5.5,5.3,5.7,5.8,5.4,5.9,5.3 \)

a) Find the critical \( \chi^{2}- \) value for a left-tailed test when \( n=11 \) and \( \alpha=0.01 \). marks] b) Find the critical \( \chi^{2}- \) value for a two-tailed test when \( n=9 \) and \( \alpha=0.05 \). marks]

The five-number summary for a data set is: Min \( =14 \quad Q_{1}=40 \quad M=55 \quad Q_{3}=62 \quad \) Max \( =99 \) a Determine the values of the upper and lower fences. b The smallest three values in the data set are \( 6,18,34 \) and the largest are \( 90,94,99 \). Which of these are outliers?