Question

if we draw the distribution and shade the proportion above the mean, which direction would we shade? step 3: find the proportion in the z - table and apply the rule. please report the final proportion after applying the correct rule procedure. p(z_final)= step 4: report the answer. please report the proportion to 4 decimal places and all other values to 2 decimal places. the probability is p = that a random sample of 4 scores will have a mean of or greater when drawn from a normal distribution having μ = and σ =

Explanation:

Step1: Understand normal - distribution shading

In a normal distribution, values above the mean are on the right - hand side. So we shade to the right.

Step2: Recall properties of the standard normal distribution

The total area under the standard normal curve is 1. The mean of the standard normal distribution (z - distribution) is 0. The proportion of the area above the mean in a standard normal distribution is 0.5.

Step3: Use the z - score formula for sample means

The z - score for a sample mean $\bar{x}$ is given by $z=\frac{\bar{x}-\mu}{\frac{\sigma}{\sqrt{n}}}$, where $\mu$ is the population mean, $\sigma$ is the population standard deviation, and $n$ is the sample size. Here $n = 4$. But since we are just asked about the proportion above the mean without specific values for $\bar{x}$, $\mu$, and $\sigma$, we know from the properties of the normal distribution that the proportion of the area above the mean of a normal distribution is 0.5000.

Answer:

The direction to shade is to the right. The proportion $p(z_{final})=0.5000$. The probability $p = 0.5000$ that a random sample of 4 scores will have a mean of the population mean or greater when drawn from a normal distribution.