A variable \( x \) is normally distributed with mean 21 and standard deviation 5. a) Determine the \( z \)-score for \( x=27 \). b) Determine the \( z \)-score for \( x=15 \). c) What value of \( x \) has a \( z \)-score of 1.8 ? \( x=x= \) d) What value of \( x \) has a \( z \)-score of -0.6 ? e) What value of \( x \) has a \( z \)-score of 0 ? \( x= \)

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?

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

University researchers published a working paper. One of the objectives of the study was to determine whether ride-share drivers actually make a profit. Data collected from a sample of 1,126 ride-share drivers yielded a mean monthly profit \( \bar{x}=\$ 661 \) with standard deviation \( s=\$ 581 \). A ride-share company executive reports that \( \mu \), the true mean monthly profit of all its rideshare drivers, is \( \$ 1,000 \). Use \( \alpha=0.01 \) to test the executive's figure. Complete parts a through e below. b. Find the rejection region for the test. Select the correct choice below and fill in the answer box(es) within your choice. (Round to two decimal places as needed.) A. \( z \) < \( z>\square \) C. \( z<\square \) or \( z>\square \)

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