Mathematics: The mean weight of trucks traveling on a particular section of i-475 is not known. a state highway inspector needs an estimate of the population mean. he selects and weighs a random sample of 49 trucks and finds the mean weight is 15.8 tons. the population standard deviation is 3.8 tons. what is the 95% confidence interval for the population mean? 14.7 and 16.9 10.0 and 20.0 16.1 and 18.1 13.2 and 17.6

The mean weight of trucks traveling on a particular

Ответ:

hall7948

14.03.2022

14.7 and 16.9

Step-by-step explanation:

We want to find the confidence interval for the mean when the population standard deviation $\sigma$ , is known so we use the confidence interval for the mean.

The following assumptions are also met;

The sample is a random sample $n\ge 30$

The z confidence interval for the mean is given by:

$\bar X-z_{\frac{\alpha}{2} }(\frac{\sigma}{\sqrt{n} } )\:$

The appropriate z-value for 95% confidence interval is 1.96 (read from the standard normal z-distribution table)....See attachment.

From the question, we have n=49 , $\sigma=3.8$ and $\bar X=15.8$

We substitute all these values to get:

$15.8-1.96(\frac{3.8}{\sqrt{49} } )\:$

$15.8-1.96(\frac{3.8}{7 } )\:$

$14.7\:$ correct to one decimal place.

The mean weight of trucks traveling on a particular section of i-475 is not known. a state highway i

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