Answer: a) (1008.34,1019.658) b) (1009.24,1018.76)
Step-by-step explanation:
Since we have given that
n = 75
mean = 1014 hours
Standard deviation = 25 hours
At 95% two sided , z = 1.96
So, confidence interval would be
![\bar{x}\pm z\dfrac{\sigma}{\sqrt{n}}\\\\=1014\pm 1.96\dfrac{25}{\sqrt{75}}\\\\=1014\pm 5.658\\\\=(1014-5.658,1014+5.658)\\\\=(1008.34,1019.658)](https://tex.z-dn.net/?f=%5Cbar%7Bx%7D%5Cpm%20z%5Cdfrac%7B%5Csigma%7D%7B%5Csqrt%7Bn%7D%7D%5C%5C%5C%5C%3D1014%5Cpm%201.96%5Cdfrac%7B25%7D%7B%5Csqrt%7B75%7D%7D%5C%5C%5C%5C%3D1014%5Cpm%205.658%5C%5C%5C%5C%3D%281014-5.658%2C1014%2B5.658%29%5C%5C%5C%5C%3D%281008.34%2C1019.658%29)
(b) Construct a 95% lower confidence bound on the mean life.
z = 1.65
So, confidence interval would be
![\bar{x}\pm z\times \dfrac{\sigma}{\sqrt{n}}\\\\=1014\pm 1.65\times \dfrac{25}{\sqrt{75}}\\\\=1014\pm 4.76\\\\=(1014-4.76,1014+4.76)\\\\=(1009.24,1018.76)](https://tex.z-dn.net/?f=%5Cbar%7Bx%7D%5Cpm%20z%5Ctimes%20%5Cdfrac%7B%5Csigma%7D%7B%5Csqrt%7Bn%7D%7D%5C%5C%5C%5C%3D1014%5Cpm%201.65%5Ctimes%20%5Cdfrac%7B25%7D%7B%5Csqrt%7B75%7D%7D%5C%5C%5C%5C%3D1014%5Cpm%204.76%5C%5C%5C%5C%3D%281014-4.76%2C1014%2B4.76%29%5C%5C%5C%5C%3D%281009.24%2C1018.76%29)
Hence, a) (1008.34,1019.658) b) (1009.24,1018.76)