Consider a manufacturing process that produces dimensional lumber of 2" by 4" with a specified target width. The length of each produced lumber follows a normal distribution with a mean of 10 feets and a standard deviation of 0.1 centimeters. The manufacturing company has set a quality control standard that requires at least 95% of the produced lumber to fall above the acceptable length threshold. Determine the acceptable length threshold above which 95% of the lumber should fall.

The diameters of bolts produced in a machine shop are normally distributed with a mean of 5.79 millimeters and a standard deviation of 0.07 millimeters. Find the two diameters that separate the top 7% and the bottom 7%. These diameters could serve as limits used to identify which bolts should be rejected. Round to the nearest hundredth if necessary.

A ski gondola carries skiers to the top of a mountain. Assume that weights of skiers are normally distributed with a mean of 186 lb and a standard deviation of 44lb. The gondola has a stated capacity of 25 ​passengers, and the gondola is rated for a load limit of 3500lb. Complete parts​ (a) through​ (d) below. A. Given that the gondola is rated for a load limit of 3500​lb, what is the maximum mean weight of the passengers if the gondola is filled to the stated capacity of 25 ​passengers? The maximum mean weight is______ B.  If the gondola is filled with 25 randomly selected​ skiers, what is the probability that their mean weight exceeds the value from part​ (a)? The probability is____ C. If the weight assumptions were revised so that the new capacity became 20 passengers and the gondola is filled with 20 randomly selected​ skiers, what is the probability that their mean weight exceeds 186 ​lb, which is the maximum mean weight that does not cause the total load to exceed 3500​lb? The…

The shelf life of a batteries produced by one major company are normally distributed with a mean of 4.3 years and a standard deviation of 0.6 years. The figure below shows the distribution of shelf lives of batteries produced by one major company. Calculate the shaded area under the curve. Answer:

Because the mean is very sensitive to extreme values, it is not a resistant measure of center. By deleting some low values and high values, the trimmed mean is more resistant. To find the 10% trimmed mean for a data set, first arrange the data in order, then delete the bottom 10% of the values and delete the top 10% of the values, then calculate the mean of the remaining values. Use axial loads (pounds) of aluminum cans listed below for cans that are 0.0111 in. thick. Identify any outliers, then compare the median, mean, 10% trimmed mean, and 20% trimmed mean. 247 261 269 273 275 280 282 282 284 285 285 287 290 292 293 296 296 299 311 507 Identify any outliers. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. OA. The outlier(s) is/are pounds. (Type a whole number. Use a comma to separate answers as needed.) C OB. There are no outliers.

While conducting experiments, a marine biologist selects water depths from a uniformly distributed collection that vary between 1.50 m and 5.50 m. What is the standard deviation of the water depth?

The weights of people in a certain population are normally distributed with a mean of 159 lb and a standard deviation of 24 lb. Determine the sampling distribution of the mean for samples of size 5.