A manufacturer of hard safety hats for construction workers is concerned about the mean and the variation of the forces its helmets transmit to wearers when subjected to a standard external force. The manufacturer desires the mean force transmitted by helmets to be 800 pounds (or less), well under the legal 1000-pound limit, and desires σ to be less than 40. Tests were run on a random sample of n = 40 helmets, and the sample mean and variance were found to be equal to 825 pounds and 2350 pounds2 , respectively. Construct a 95% confidence interval for the population variance.

Step-by-step explanation:

Hello!

You need to construct a 95% CI for the population variance of the forces the safety helmets transmit to wearers.

The variable of interest is X: Force a helmet transmits its wearer when an external force is applied (pounds)

Assuming this variable has a normal distribution, the manufacturer expects it to have a mean of μ= 800 pounds and a standard deviation of σ= 40 pounds

A test sample of n=40 was taken and the resulting mean and variance are:

X[bar]= 825 pounds

S²= 2350 pounds²

To estimate the population variance per confidence interval you have to use the following statistic:

And the CI is calculated as:

[;]

[;]

[1577.45; 3867.09] pounds²

Using a confidence level of 95% you'd expect that the interval [1577.45; 3867.09] pounds² contains the value of the population variance of the force the safety helmets transmit to their wearers when an external force is applied.

I hope this helps!

d. bc = 12 and ef = 16

step-by-step explanation:

we are given that δabc : δdef such that .

also, it is given that

so, from the options, we need that .

a.

b.

c.  

d.

as, we can see that only option d gives the same ratio as i.e. .

hence, the possible lengths are bc = 12 and ef = 16.