Introduction to Statistics / MAT300 SPRING 2014
1.Chebyshev’s theorem and the empirical rule
BIG Corporation produces just about everything but is currently interested in the lifetimes of its batteries, hoping to obtain its share of a market boosted by the popularity of portable CD and MP3 players. To investigate its new line of Ultra batteries, BIG randomly selects Ultra batteries and finds that they have a mean lifetime of hours. Suppose that this mean applies to the population of all Ultra batteries. Complete the following statements about the distribution
of lifetimes of all Ultra batteries.
(a) According to Chebys hev’s theorem , at least ? of the lifetim es lie within 1.5 s tandard deviations of the m ean, 890 hours .
(b) Suppos e that the dis tribution is bell-s haped. If approxim ately 68% of the lifetim es lie between 795 hours and 985 hours , then the approxim ate value of the s tandard deviation for the dis tribution, according to the em pirical rule, is .
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In this discussion, you will simplify and compare equivalent expressions written both in radical form and with rational (fractional) exponents. Read the following instructions in order and view the example to complete this discussion:
· Find the rational exponent problems assigned to you in the table below.
|If the last letter of your first name is||On pages 576 – 577, do the following problems|
|A or L||42 and 101|
|B or K||96 and 60|
|C or J||46 and 104|
|D or I||94 and 62|
|E or H||52 and 102|
|F or G||90 and 64|
|M or Z||38 and 72|
|N or Y||78 and 70|
|O or X||44 and 74|
|P or W||80 and 68|
|Q or V||50 and 76|
|R or U||84 and 66|
|S or T||54 and 100|
· Simplify each expression using the rules of exponents and examine the steps you are taking.
· Incorporate the following five math vocabulary words into your discussion. Use bold font to emphasize the words in your writing (Do not write definitions for the words; use them appropriately in sentences describing the thought behind your math work.):
o Principal root
o Product rule
o Quotient rule
o nth root
Refer to Inserting Math Symbols for guidance with formatting. Be aware that with regards to the square root symbol, you will notice that it only shows the front part of a radical and not the top bar. Thus, it is impossible to tell how much of an expression is included in the radical itself unless you use parenthesis. For example, if we have √12 + 9 it is not enough for us to know if the 9 is under the radical with the 12 or not. Thus we must specify whether we mean it to say √(12) + 9 or √(12 + 9). As there is a big difference between the two, this distinction is important in your notation.
Another solution is to type the letters “sqrt” in place of the radical and use parenthesis to indicate how much is included in the radical as described in the second method above. The example above would appear as either “sqrt(12) + 9” or “sqrt(12 + 9)” depending on what we needed it to say.
Your initial post should be at least 250 words in length. Support your claims with examples from required material(s) and/or other scholarly resources, and properly cite any references. Respond to at least two of your classmates’ posts by Day 7.
Carefully review the Grading Rubric for the criteria that will be used to evaluate your discussion.