MATH SOLVE

2 months ago

Q:
# For a new product, you need to determine the average diameter of a specialized electronic component, which will be a critical component of the new product. You measure the diameter in a sample of size 15 and find an average diameter of 0.24 mm, with a standard deviation of 0.02 mm. Other studies indicate that the diameter of similar products is normally distributed. The 99% confidence interval for the average diameter of this electronic component is ______.0.232 to 0.2480.230 to 0.2500.228 to 0.2520.26 to 0.2540.224 to 0.256

Accepted Solution

A:

Answer: 0.224 to 0.256Step-by-step explanation:As per given , we haven= 15df = 14 (df=n-1)[tex]\overline{x}=0.24\\ s=0.02[/tex]Significance interval : [tex]\alpha: 1-0.99=0.01[/tex]Since , population standard deviation is unknown , so we use t-test .Using t-value table , [tex]t_{df,\ \alpha/2}=t_{14,\ 0.005}=2.977[/tex]99% Confidence interval will be :[tex]\overline{x}\pm t_{df,\ \alpha/2}\dfrac{s}{\sqrt{n}}[/tex][tex]0.24\pm (2.977)\dfrac{0.02}{\sqrt{15}}[/tex][tex]\approx0.24\pm 0.015[/tex][tex]=(0.24- 0.015,\ 0.24+ 0.015)=(0.225,\ 0.255)[/tex]Hence, The 99% confidence interval for the average diameter of this electronic component is 0.225 to 0.255.As we check all the given options , the only closest option is 0.224 to 0.256.So the correct answer is 0.224 to 0.256.