A group of engineers developed a new design for a steel cable. They need to estimate the amount of weight the cable can hold. The weight limit will be reported on cable packaging. The engineers take a random sample of 48 cables and apply weights to each of them until they break. The 48 cables have a mean breaking weight of 773 lb. The standard deviation of the breaking weight for the sample is 16.1 lb. Find the 95% confidence interval to estimate the mean breaking weight for this type cable.

The 95%   confidence interval is  

Step-by-step explanation:

From the question we are told that  

    The  sample size is n = 48

    The sample mean is  

     The standard deviation is  

Now given that the confidence level is  95% , then the level of significance is mathematically represented as

Next we obtain the  critical value of   from the normal distribution table , the value is

The reason we are obtaining critical values of   instead of     is because  

represents the area under the normal curve where the confidence level interval (   ) did not cover which include both the left and right tail while

is just the area of one tail which what we required to calculate the margin of error

 The  margin of error is mathematically represented as

substituting values

The 95% confidence interval to estimate the mean breaking weight for this type cable is mathematically evaluated as

substituting values

is there any photos or whatever?

step-by-step explanation:

we have

using a graphing tool

see the attached figure

this is a quadratic equation (vertical parabola) open up

the vertex is a > vertex

the domain of the function is all real > interval (-∞,∞)

the range of the function is the > [-6.125,∞)

the function has two x->   and

the function is increasing over the > (0.25,∞)

the function is decreasing over the > (-∞,0.25)