Answer:
See below
Step-by-step explanation:
<u>Rayovac type-D batteries
</u>
<u>Mean
</u>
= 21 h
<u>Standard deviation
</u>
= 1.38 h
<em />
Find the probability (to four places after the decimal) that a single Rayovac battery lasts under 22 hours:
<em>Here we use the Normal N(0,1)
</em>
To find this value use either a table or a spreadsheet.
In Excel
<em>NORMDIST(0.7246,0,1,1)
</em>
In OpenOffice Calc
<em>NORMDIST(0.7246;0;1;1)
</em>
Whenever we have a sample size less than 30, we will be using the Student's t distribution with (sample size -1) degrees of freedom instead of the Normal.
Find the probability that the mean "continuous use-life" of 4 randomly selected Rayovac batteries is less than 22 hours:
To find this value use either a table or a spreadsheet.
In Excel
<em>1-TDIST(1.4493,3,1)
</em>
In OpenOffice Calc
<em>1-TDIST(1.4493;3;1)
</em>
Find the probability that the mean "continuous use-life" of 16 randomly selected Rayovac batteries is less than 22 hours:
To find this value use either a table or a spreadsheet.
In Excel
<em>1-TDIST(2.8986,15,1)
</em>
In OpenOffice Calc
<em>1-TDIST(2.8986 ;15;1)
</em>
Find the probability that the mean "continuous use-life" of 64 randomly selected Rayovac batteries is less than 22 hours:
<em>Since the sample size is greater than 30 we can use back the Normal
</em>
To find this value use either a table or a spreadsheet.
In Excel
<em>NORMDIST(5.7971,0,1,1)
</em>
In OpenOffice Calc
<em>NORMDIST(5.7971;0;1;1)
</em>
<u>Duracell type-D batteries
</u>
<u>Mean
</u>
= 24 h
<u>Standard deviation
</u>
= 2.13 h
Find the probability that a single Duracell battery lasts under 22 hours
<em>Here we use the Normal N(0,1)
</em>
To find this value use either a table or a spreadsheet.
In Excel
<em>NORMDIST(-0.9390,0,1,1)
</em>
In OpenOffice Calc
<em>NORMDIST(-0.9390;0;1;1)
</em>
<em>
</em>
Find the probability that the mean "continuous use-life" of 4 randomly selected Duracell batteries is less than 22 hours:
To find this value use either a table or a spreadsheet.
In Excel
<em>TDIST(1.8779,3,1)
</em>
In OpenOffice Calc
<em>TDIST(1.8779;3;1)
</em>
<em>
</em>
Find the probability that the mean "continuous use-life" of 9 randomly selected Duracell batteries is less than 22 hours:
To find this value use either a table or a spreadsheet.
In Excel
<em>TDIST(2.8169,8,1)
</em>
In OpenOffice Calc
<em>TDIST(2.8169;8;1)
</em>
Find the probability that the mean "continuous use-life" of 25 randomly selected Duracell batteries is less than 22 hours:
To find this value use either a table or a spreadsheet.
In Excel
<em>TDIST(4.6948,24,1)
</em>
In OpenOffice Calc
<em>TDIST(4.6948;24;1)
</em>
<em />
Find the probability that a randomly selected Rayovac battery lasts longer than a randomly selected Duracell battery given random samples of four of each kind.