A population of values has a normal distribution with \( \mu=243.7 \) and \( \sigma=69.6 \). You intend to draw a random sample of size \( n=81 \). Find the probability that a single randomly selected value is between 256.8 and 265.4 . \( P(256.8<X<265.4)=\square \) Find the probability that a sample of size \( n=81 \) is randomly selected with a mean between 256.8 and 265.4 . \( P(256.8<M<265.4)=\square \) Enter your answers as numbers accurate to 4 decimal places. Answers obtained using exact \( z \)-scores or \( z \) - scores rounded to 3 decimal places are accepted.

A variable \( x \) is normally distributed with mean 21 and standard deviation 5. a) Determine the \( z \)-score for \( x=27 \). b) Determine the \( z \)-score for \( x=15 \). c) What value of \( x \) has a \( z \)-score of 1.8 ? \( x=x= \) d) What value of \( x \) has a \( z \)-score of -0.6 ? e) What value of \( x \) has a \( z \)-score of 0 ? \( x= \)

PENSAMIENTO MATEMÁTICO 1 3. Homero acaba de abrir una bolsa de chocolates confitados y los clasifica por color encontrando 5 naranjas, 7 verdes, 6 azules, 8 amarillos, 5 rojos, y 6 cafés. Realiza una gráfica de columnas para representar lo que encontró en la bolsa -

1.3.1 Bereken die gemiddelde aantal huishoudings in Suid-Afrika wat gedurende 2022 nie toegang tot die internet gehad het nie.

A variable is normally distributed with mean 18 and standard deviation 9 . Use your graphing calculator to find each of the following areas. Write your answers in decimal form. Round to the nearest thousandth as needed. a) Find the area to the left of 17.

EJERCICIO 7 -1 Se muestran las tallas de calzado de los últimos 20 clientes que han entrado a una zapatería \[ \begin{array}{l}25,22.5,26,26.5,27,25,23,24,24,23,24,24.5,24.5,24,23.5,24.5 \\ 23.5,24.5,25,23.5\end{array} \] Ordena las tallas y elabora una gráfica de columnas para representar los datos