Consumer Reports uses a 100-point customer satisfaction score to rate the nations major chain stores. Assume that from the past experience with the satisfaction rating score, a population standard deviation of 12 is expected. In 2012, Costco with its 432 warehouses in 40 states was the only chain store to earn an outstanding rating for overall quality. A sample of 15 costco customer satisfaction scores follow:95 90 83 64 9598 80 83 82 9386 80 94 75 62(A) What is the sample mean customer satisfaction score for Costco?(B) What is the sample variance?(C) What is the sample standard deviation?
Accepted Solution
A:
Answer:(A) Mean = 84(B) Variance = 118.714(C) Standard deviation = 10.89Step-by-step explanation:Data provided:number of observations, n = 15sample of 15 costco customer satisfaction scores followX [tex]X-\bar{X}[/tex] [tex](X-\bar{X})^2[/tex]95 11 12190 6 3683 -1 164 -20 40095 11 12198 14 19680 -4 1683 -1 182 -2 493 9 8186 2 480 -4 1694 10 10075 -9 8162 -22 484================================================ ∑X = 1260 ∑= 1662Now, (A) Mean = [tex]\frac{\textup{Sum of all observations}}{\textup{Total number of observations}}[/tex]orMean = [tex]\frac{\textup{1260}}{\textup{15}}[/tex] = 84(B) Variance = [tex]\frac{\sum(X-\bar{X})^2}{n-1}[/tex]orVariance = [tex]\frac{1662}{15-1}[/tex]orVariance = 118.714 (C) Standard deviation = √Variance = √118.714 = 10.89