Question

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?

Answer 1

(14.7 , 16.9)

Explanation:

it is given that
`\bar{x}=15.8` tons

σ=3.8 tons

n=49

at 95% confidence level α=1-.95=0.05

`z_(\alpha )/(2)=z_(0.05)/(2)=z_(0.025)\\`

=1.96 ( from the standard table)

at 95% confidence level the coefficient interval for μ is

`\bar{x}\pm z_(\alpha )/(2)* (\sigma )/(√(n))`

`15.8\pm 1.96* (3.8)/( √(49))`

`15.8\pm 1.1`

(14.7, 16.9)