Question

Problem 1. (1 point) Fluorescent lightbubs have let me that follow a normal distribution, with an average of 1,735 days and a standard deviation of 1,702 hours. In the production por the manufacturer dress randon samples of 107 lights and determines the meantime of the sample What is the standard deviation, in hours of this same mean? Answer Note: round your answers to 2 decimal places

Answer 1

Answer:-

Given That:-

Fluorescent lightbulbs have lifetimes that follow a normal distribution, with an average life of 1,735 days and a standard deviation of 1,702 hours In the production process the manufacturer draws random samples of 107 lightbulbs and determines the mean lifetime of the sample. What is the standard deviation, in hours, of this sample mean?

Given,

Let X = Lifetimes of Fluoroscent Light bulbes

Given,

X ~ Normal $(\mu, \sigma^2)$

$\mu=$ 1735

$, \sigma^2=1702$

Then we know for sample of size n, sample mean is  $\bar{X}$ and $\bar{X}\sim Normal(\mu, \frac{\sigma^2}{n})$

Mean ($\bar{X}$) =  $\mu$

Standard deviation ($\bar{X}$)   $=\frac{\sigma}{\sqrt{n}}$

Here,

n = 107

Mean = 1735

Stanadard deviation ($\bar{X}$) = 1702/$\sqrt{107}$

= 164.538

= 164.54

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