If you take a sample of size 39 , can you say what the shape of the distribution of the sample mean is? Why? If the sample size is 39 , then you can say the sampling distribution of the sample mean is not normally distributed since the sample size is greater than 30 . If the sample size is 39 , then you can't say anything about the sampling distribution of the sample mean, since the population of the random variable is not normally distributed and the sample size is greater than 30.

\( 1 \leftarrow \begin{array}{l}\text { Researchers conducted a study on using a chief executive officer's facial structure to predict a firm's financial } \\ \text { performance. The facial width-to-height ratio (WHR) for each in a sample of } 52 \text { CEOs at publicly traded firms was } \\ \text { determined. The sample resulted in } \bar{x}=1.55 \text { and } s=0.36 \text {. An analyst wants to predict the financial performance of a } \\ \text { firm based on the value of the true mean facial WHR of CEOs. The analyst wants to use the value of } \mu=2.1 \text {. Do yo } \\ \text { recommend he use this value? Conduct a test of hypothesis for } \mu \text { to help you answer the question. Specify all the } \\ \text { elements of the test, including } H_{0}, H_{a} \text {, test statistic, } p \text {-value, and your conclusion. Test at } \alpha=0.01 \text {. } \\ \text { What is the value of the test statistic? } \\ z=-11.02 \text { (Round to two decimal places as needed.) } \\ \text { Find the p-value. } \\ \text { p-value }=\square \text { (Round to three decimal places as needed.) }\end{array} \).

A random sample of 69 produced the summary statistics \( \bar{x}=0.326 \) and \( s^{2}=0.064 \). Complete parts a and \( \mathbf{b} \). b. Test the null hypothesis that \( \mu=0.37 \) against the alternative hypothesis that \( \mu \neq 0.37 \), using \( \alpha=0.10 \). What is the value of the test statistic? F=-1.44 (Round to two decimal places as needed.) Find the p-value. (Round to three decimal places as needed.)

A variable \( x \) is normally distributed with mean 22 and standard deviation 3. Round your answers to the nearest hundredth as needed. a) Determine the \( z \)-score for \( x=27 \). b) Determine the \( z \)-score for \( x=20 \). c) What value of \( x \) has a \( z \)-score of 2.33 ? d) What value of \( x \) has a \( z \)-score of -0.3 ? \( x= \) e) What value of \( x \) has a \( z \)-score of 0 ?

The annual rainfall in a certain region is approximately normally distributed with mean 42.6 inches and standard deviation 5.7 inches. Round answers to the nearest tenth of a percent. a) What percentage of years will have an annual rainfall of less than 44 inches? b) What percentage of years will have an annual rainfall of more than 40 inches? c) What percentage of years will have an annual rainfall of between 39 inches and 43 inches? Question Help: \( \quad \) Read Video

A variable \( x \) is normally distributed with mean 21 and standard deviation 8 . Round your answers to the nearest hundredth as needed. a) Determine the \( z \)-score for \( x=27 \). \[ z=0.75 \] b) Determine the \( z \)-score for \( x=16 \). \[ z= \]