Question

The weight of trucks traveling on a particular section of I-475 have a population mean of 15.8 tons and a population standard deviation of 4.2 tons. What is the probability a state highway inspector could select a sample of 49 trucks and find the sample mean to be 14.3 tons or less

Answer 1

Answer: 0.0062

Step-by-step explanation:

Given : The weight of trucks traveling on a particular section of I-475 have a population mean of $\mu=15.8$ tons and a population standard deviation of $\sigma=4.2$ tons.

Sample size : n=49

Let x be the random variable that represents the weight of trucks .

z-score : $z=\dfrac{x-\mu}{\dfrac{\sigma}{\sqrt{n}}}$

For x= 14.3 tons

$z=\dfrac{14.3-15.8}{\dfrac{4.2}{\sqrt{49}}}\approx-2.5$

Now, the probability a state highway inspector could select a sample of 49 trucks and find the sample mean to be 14.3 tons or less will be :-

$P(X\leq14.3)=P(z$

Hence, the probability a state highway inspector could select a sample of 49 trucks and find the sample mean to be 14.3 tons or less =0.0062