In a survey of a group of men, the heights in the 20 - 29 age group were normally distributed, with a mean of 67.4 inches and a standard deviation of 3.0 inches. A study participant is randomly selected. Complete parts (a) through (d) below. (a) Find the probability that a study participant has a height that is less than 67 inches. The probability that the study participant selected at random is less than 67 inches tall is (b) Find the probability that a study participant has a height that is between 67 and 70 inches. The probability that the study participant selected at random is between 67 and 70 inches tall is \( \square \). (Round to four decimal places as needed.) (c) Find the probability that a study participant has a height that is more than 70 inches. The probability that the study participant selected at random is more than 70 inches tall is \( \square \). (Round to four decimal places as needed.) (d) Identify any unusual events. Explain your reasoning. Choose the correct answer below. A. The events in parts (a), (b), and (c) are unusual because all of their probabilities are less than 0.05 . The events in parts (a) and (c) are unusual because its probabilities are less than 0.05 . C. There are no unusual events because all the probabilities are greater than 0.05. D. The event in part (a) is unusual because its probability is less than 0.05 .

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

Consider the Standard Normal distribution. The mean is always \( \square \) and the standard deviation is always

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.

In a normal distribution, a data value located 1.4 standard deviations below the mean has Standard Score: \( \mathrm{z}=-1.4 \) In a normal distribution, a data value located 2.3 standard deviations above the mean has Standard Score: \( \mathrm{z}=2.3 \) In a normal distribution, the mean has Standard Score: \( \mathrm{z}=\square \)

a class of 40 learners, 32 take Mathematics, 23 Hist ot take Mathematics or History. Draw a Venn diagram to illustrate the given information How many learners take Mathematics and History Determine the Following: the probability that a learner takes History and Mathen the probability that a learner does not take Mathematic How many learners take History but not Mathematics?