Managers at an automobile manufacturing plant would like to estimate the mean completion time of an assembly line operation, . The managers plan to choose a random sample of completion times and estimate via the sample. Assuming that the standard deviation of the population of completion times is minutes, what is the minimum sample size needed for the managers to be confident that their estimate is within minutes of

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Cricetus Cricetus · Answer 1 · 2021-06-24T12:40:07+02:00

Answer:

The appropriate answer is "144".

Step-by-step explanation:

Given:

Population standard deviation,

[tex]\sigma=10.4[/tex]

Margin of error,

[tex]E=1.7[/tex]

[tex]CL=95[/tex] %

[tex]CL=1-\alpha[/tex]

Or,

[tex]\alpha=1-CL[/tex]

[tex]=1-0.95[/tex]

[tex]=0.05[/tex]

Now,

Critical value,

= [tex]Z_{\frac{\alpha}{2} }[/tex]

= [tex]Z_{\frac{0.05}{2} }[/tex]

= [tex]1.96[/tex]

The minimum sample size will be:

⇒ [tex]n=\frac{Z^2_{\frac{\alpha}{2} }(\sigma)^2}{E^2}[/tex]

By putting the values, we get

[tex]=\frac{(1.96)^2(10.4)^2}{(1.7)^2}[/tex]

[tex]=\frac{415.5074}{2.89}[/tex]

[tex]=143.774[/tex]

or,

[tex]=144[/tex]