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The life in hours of a 75-watt light bulb is known to be approximately normally distributed, with standard deviation of 25 hours. A random sample of 62 light bulbs has a mean life of 1014 hours. Construct a 98% confidence interval around the true population mean life of the light bulb.

Respuesta :

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Answer:

385

Step-by-step explanation:

We have to find the Sample size through the formula of Margin Error.

The formula is,

[tex]ME = z * \frac{\sigma}{\sqrt{n}}[/tex]

We have all the values,

ME = 2.5 hours

[tex]\sigma = 25[/tex]

cl = 98% that is in Z-table equal to 2.32

Replacing,

[tex]2.5= 2.32 * \frac{25}{\sqrt{n}}[/tex]

clearing n,

[tex]n= (1.96*\frac{25}{2.5})^2[/tex]

[tex]n= 384.16[/tex]

So the least sample size is at least of 385.