Question

In Exercises 5–8, use the following two control charts that result from testing batches of newly manufactured aircraft altimeters, with 100 in each batch. The original sample values are errors (in feet) obtained when the altimeters are tested in a pressure chamber that simulates an altitude of 6000 ft. The Federal Aviation Administration requires an error of no more than 40 ft at that altitude.

What is the value of\(\bar \bar x\)? In general, how is a value of\(\bar \bar x\)found?

Short answer

The value of\(\bar \bar x\)is equal to 2.24 feet.

The general formula to compute the value of\(\bar \bar x\)is as follows:

\(\bar \bar x = \frac{{{{\bar x}_1} + {{\bar x}_2} + ... + {{\bar x}_N}}}{N}\)

Here,

\({\bar x_i}\)and N represent the mean of the ith sample and the total number of samples, respectively.

Step-by-step solution

Given information

When aviation altimeters are tested in a pressure chamber, the \(\bar x\)chart is plotted to show the measurement of errors (in feet). The sample size for each individual is 100.

Step 2:Value of \(\bar \bar x\)

By observing the\(\bar x\)chart, the value of\(\bar \bar x\)is written on the left side beside the centerline.

Thus, the value of\(\bar \bar x\)is equal to 2.24 feet.

First, calculate the average ( or mean) of each of the subgroups and then obtain the mean of subgroups means.

The general formula to compute the value of\(\bar \bar x\)is as follows:

\(\bar \bar x = \frac{{{{\bar x}_1} + {{\bar x}_2} + ... + {{\bar x}_N}}}{N}\),where

\({\bar x_i}\)is the mean of the ith sample, and

N is the total number of samples.