2. Una empresa de investigación de mercados desea calcular el tamaño de muestra de hogar, para determinar en qué proporción de hogares por lo menos uno de sus miembros ve un programa determinado de televisión. En esa comunidad hay un total de 500 hogares. El investigador desea que su estimación esté a 0.04 de la programación verdadera (máximo error permitido), con un \( 90 \% \) de confianza. En una muestra piloto de 15 hogares 7 de los entrevistados indicaron que alguien en su casa ve regularmente dicho programa. ¿Cuál es el tamaño de muestra? Explique. 18 puntos

A water bottling facility has a mean bottling rate of 34.1 thousand bottles per hour with a standard deviation of 2.13 thousand bottles. A nearby cola bottling facility has a mean bottling rate of 25.7 thousand bottles per hour with a standard deviation of 1.63 thousand bottles. One Wednesday from noon to \( 1: 00 \) p.m, the water bottling facility bottled 37.2 thousand bottles of water, and the cola bottling facility bottled 27.7 thousand bottles of cola. Which facility increased their efficiency more during that hour? Answer

Find the range of the following data set. Assume the data set is a sample. \[ 43 \quad \begin{array}{lllllllll}54 & 51 & 86 & 39 & 51 & 52 & 45 & 81 & 46\end{array} 46 \]

Suppose that shoe sizes of American women have a bell-shaped distribution with a mean of 8.06 and a standard deviation of 1.52 . Using the empirical rule, what percentage of American women have shoe sizes that are greater than 9.58 ? Please do not round your answer.

A water bottling facility has a mean bottling rate of 34.1 thousand bottles per hour with a standard deviation of 2.13 thousand bottles. A nearby cola bottling facility has a mean bottling rate of 25.7 thousand bottles per hour with a standard deviation of 1.63 thousand bottles. One Wednesday from noon to \( 1: 00 \) p.m., the water bottling facility bottled 37.2 thousand bottles of water, and the cola bottling facility bottled 27.7 thousand bottles of cola. Which facility increased their efficiency more during that hour? Answer

Scores on a test have a mean of 89 and a standard deviation of 7 . Calvin has a score of 79. Convert Calvin's score to a \( z \)-score, rounded to the nearest hundredth.