Answer:
a
[tex]n = 640 .4[/tex]
b
[tex]n = 283.2[/tex]
Step-by-step explanation:
From the question we are told that
The population mean [tex]\= x = 0.90[/tex]
The confidence level [tex]\beta = 0.90[/tex]
The range of the observation [tex]R = 44-36 = 8[/tex]
First we obtain the z-score of [tex]\beta[/tex] which is [tex]z = 1.6449[/tex] this is obtained from the z-table
Generally the standard deviation is mathematically represented as
[tex]\sigma = \frac{R}{4}[/tex]
substituting values
[tex]\sigma = \frac{8}{4}[/tex]
[tex]\sigma = 2[/tex]
Now the sample size is mathematically represented as
[tex]n = [ z * \frac{\sigma}{\= x} ]^2[/tex]
substituting values
[tex]n = [ 1.6449 * \frac{2}{0.13} ]^2[/tex]
[tex]n = 640 .4[/tex]
When the range is equal to [tex]6 \sigma[/tex] it implies that
[tex]R = 6 \sigma = 8[/tex]
=> [tex]\sigma = \frac{8}{6}[/tex]
=> [tex]\sigma = 1.333[/tex]
So the sample size is mathematically represented as
[tex]n = [ 1.6449 * \frac{1.33}{0.13} ]^2[/tex]
[tex]n = 283.2[/tex]
