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 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 greater than or equal to 66 .

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

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 1.2 standard deviations below the mean has Standard Score: \( \mathrm{z}=\square \) In a normal distribution, a data value located 2.4 standard deviations above the mean has Standard Score: \( \mathrm{z}=\square \) In a normal distribution, the mean has Standard Score: \( \mathrm{z}=\square \)