The mean weight of a box of cereal filled by a machine is 17.0 ounces, with a standard deviation of 0.3 ounce. If the weights of all the boxes filled by the machine are normally distributed, what percent of the boxes will weigh the following amounts? (Round your answers to two decimal places.) (a) less than 16.6 ounces (b) between 16.7 and 17.3 ounces

a. What is the difference between the number who prefer the cola to the lemon flavour? b. How many Grade 4D learners were questioned altogether?

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

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

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

A 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 \( x=16 \). \[ z= \]