Question

HELP!!! STATS!!!

Answer 1

Answer:

The 99% confidence interval is   $165.776 < \mu < 180.224$  

Step-by-step explanation:

From the question we are told that

     The sample size is  n  = 100

     The sample mean is  $\= x = 173 \ days$

      The population standard deviation is  $\sigma = 28 \ days$  

From the question we are told the confidence level is  99% , hence the level of significance is    

      $\alpha = (100 - 99 ) \%$

=>   $\alpha = 0.01$

Generally from the normal distribution table the critical value  of  $\frac{\alpha }{2}$ is  

   $Z_{\frac{\alpha }{2} } = 2.58$

Generally the margin of error is mathematically represented as  

      $E = Z_{\frac{\alpha }{2} } * \frac{\sigma }{\sqrt{n} }$

      $E = 2.58 * \frac{28 }{\sqrt{100} }$

=>    $E = 7.224$

Generally 95% confidence interval is mathematically represented as  

      $\= x -E < \mu < \=x +E$

=>     $173 -7.224 < \mu < 173 + 7.224$    

=>     $165.776 < \mu < 180.224$