91Ó°ÊÓ

True or False: A normal score is the expected z-score of a data value, assuming the distribution of the random variable is normal.

True or False: The normal curve is symmetric about its mean, \(\mu .\)

Use the results in the table to (a) draw a normal probability plot, (b) determine the linear correlation between the observed values and expected z-scores, (c) determine the critical value in Table VI to assess the normality of the data $$ \begin{array}{cccc} \text { Index, } i & \text { Observed Value } & f_{i} & \text { Expected } z \text { -score } \\ \hline 1 & 1 & 0.09 & -1.34 \\ \hline 2 & 3 & 0.22 & -0.77 \\ \hline 3 & 6 & 0.36 & -0.36 \\ \hline 4 & 8 & 0.50 & 0 \\ \hline 5 & 10 & 0.64 & 0.36 \\ \hline 6 & 13 & 0.78 & 0.77 \\ \hline 7 & 35 & 0.91 & 1.34 \end{array} $$

Find the indicated areas. For each problem, be sure to draw a standard normal curve and shade the area that is to be found. Determine the area under the standard normal curve that lies to the left of (a) \(z=-3.49\) (b) \(z=-1.99\) (c) \(z=0.92\) (d) \(z=2.90\)

Use a normal probability plot to assess whether the sample data could have come from a population that is normally distributed. O-Ring Thickness A random sample of O-rings was obtained, and the wall thickness (in inches) of each was recorded. $$\begin{array}{lllll} \hline 0.276 & 0.274 & 0.275 & 0.274 & 0.277 \\ \hline 0.273 & 0.276 & 0.276 & 0.279 & 0.274 \\ \hline 0.273 & 0.277 & 0.275 & 0.277 & 0.277 \\ \hline 0.276 & 0.277 & 0.278 & 0.275 & 0.276 \\ \hline \end{array}$$

Find the indicated areas. For each problem, be sure to draw a standard normal curve and shade the area that is to be found. Determine the area under the standard normal curve that lies to the right of (a) \(z=-3.49\) (b) \(z=-0.55\) (c) \(z=2.23\) (d) \(z=3.45\)

Use a normal probability plot to assess whether the sample data could have come from a population that is normally distributed. Customer Service A random sample of weekly work logs at an automobile repair station was obtained, and the average number of customers per day was recorded. $$\begin{array}{lllll} \hline 26 & 24 & 22 & 25 & 23 \\ \hline 24 & 25 & 23 & 25 & 22 \\ \hline 21 & 26 & 24 & 23 & 24 \\ \hline 25 & 24 & 25 & 24 & 25 \\ \hline 26 & 21 & 22 & 24 & 24 \\ \hline \end{array}$$

Find the indicated areas. For each problem, be sure to draw a standard normal curve and shade the area that is to be found. Determine the area under the standard normal curve that lies between (a) \(z=-2.55\) and \(z=2.55\) (b) \(z=-1.67\) and \(z=0\) (c) \(z=-3.03\) and \(z=1.98\)

Chips per Bag In a 1998 advertising campaign, Nabisco claimed that every 18-ounce bag of Chips Ahoy! cookies contained at least 1000 chocolate chips. Brad Warner and Jim Rutledge tried to verify the claim. The following data represent the number of chips in an 18 -ounce bag of Chips Ahoy! based on their study. $$ \begin{array}{lllll} \hline 1087 & 1098 & 1103 & 1121 & 1132 \\ \hline 1185 & 1191 & 1199 & 1200 & 1213 \\ \hline 1239 & 1244 & 1247 & 1258 & 1269 \\ \hline 1307 & 1325 & 1345 & 1356 & 1363 \\ \hline 1135 & 1137 & 1143 & 1154 & 1166 \\ \hline 1214 & 1215 & 1219 & 1219 & 1228 \\ \hline 1270 & 1279 & 1293 & 1294 & 1295 \\ \hline 1377 & 1402 & 1419 & 1440 & 1514 \\ \hline \end{array} $$ (a) Draw a normal probability plot to determine if the data could have come from a normal distribution. (b) Determine the mean and standard deviation of the sample data. (c) Using the sample mean and sample standard deviation obtained in part (b) as estimates for the population mean and population standard deviation, respectively, draw a graph of a normal model for the distribution of chips in a bag of Chips Ahoy! (d) Using the normal model from part (c), find the probability that an 18-ounce bag of Chips Ahoy! selected at random contains at least 1000 chips. (e) Using the normal model from part (c), determine the proportion of 18 -ounce bags of Chips Ahoy! that contains between 1200 and 1400 chips, inclusive.

Find the indicated z-score. Be sure to draw a standard normal curve that depicts the solution. Find the \(z\) -score such that the area under the standard normal curve to its left is 0.2 .