Will the sampling distribution of \( \bar{x} \) always be approximately normally distributed? Explain. Choose the correct answer below. A. Yes, because the Central Limit Theorem states that the sampling distribution of \( \bar{x} \) is always approximately normally distributed. B. No, because the Central Limit Theorem only states that the sampling distribution of \( \bar{x} \) is approximately normally distributed if the sample size is large enough. C. No, because the Central Limit Theorem states that the sampling distribution of \( \bar{x} \) is approximately normally distributed only if the population being sampled is normally distributed. D. No, because the Central Limit Theorem only states that the sampling distribution of \( \bar{x} \) is approximately normally distributed if the sample size is more than \( 5 \% \) of the population.

Which of the following statements are TRUE about the Normal Distribution? Check all that apply. The graph of the Normal Distribution is bell-shaped, with tapering tails that never actually touch the horizontal axis. \( 50 \% \) of the data values lie at or above the mean. about \( 95 \% \) of all data values lie within 1 standard deviation of the mean. The mean, median and mode are all equal and occur at the center of the distribution. Data values are spread evenly around the mean. Data values farther from the mean are less common than data values closer to the mean.

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 set of exam scores is normally distributed with a mean \( =74 \) and standard deviation \( =8 \). \( 95 \% \) of the data values lie between 58 \( \% \) of the exam scores are between 66 and 74 . \( \% \) of the exam scores are between 74 and 90 . \( \% \) of the exam scores are between 82 and 90 . \% oxam scores are greater than or equal to 66 .