Afire insurance company wishes to study the amount of fire damage in major residential fires. the data they collected from a simple random sample of fires in the past six months are shown below: damage (in thousands of dollars) 26.2 17.8 23.1 36.0 31.1 43.2 36.4 26.1 the fire chief wishes to estimate the mean amount of damage with a 95% confidence interval. the population is normally distributed. what is the left bound of the 95% confidence interval for the true population mean (rounded to 2 decimal places)?

23.08 < µ < 36.9

Step-by-step explanation:

First we need to find the sample mean and standard deviation.  

Sample mean:  Add up the values and divide by the total amount of values...

(26.2 + 17.8 + 23.1 + 36.0 + 31.1 + 43.2 + 36.4 + 26.1)/8 = 239.9/8 = 29.99

The sample standard deviation is calculated on the first attached photo

s = 8.27

The confidence interval is constructed in the second attached photo

alright so i think for this one it would to draw it out. this may be hard for me to try and draw, but i will do my best on here:

        r

  /       |     \

notice how it forms 2 triangles inside one bigger triangle.

so if we know the angle spr is the same as psr that is saying the measure of angle p is the same as angle s. this means the big triangle psr is either isosceles or equilateral. in both cases, the triangle is perfectly symmetrical when split down the middle, which is in this case rq. because we know it is perfectly symmetrical on both sides, we know that the two triangles inside the bigger one are equal.