Final answer:
a. The mean monthly electric bill is $112.80. b. The range is $62. c. The variance is 38.936. d. The standard deviation is approximately 6.24.
Step-by-step explanation:
a. Mean: To find the mean, we add up all the monthly electric bills and divide by the total number of months. 115 + 150 + 144 + 126 + 90 + 90 + 95 + 110 + 120 + 88 = 1128. Then we divide 1128 by 10 (the number of months) to get the mean: $112.80.
b. Range: To find the range, we subtract the smallest value from the largest value. The smallest value is 88 and the largest value is 150, so the range is 150 - 88 = $62.
c. Variance: To find the variance, we need to find the squared difference between each monthly bill and the mean. Then we add up all those squared differences and divide by the total number of months. The squared differences are: (115-112.8)^2, (150-112.8)^2, (144-112.8)^2, (126-112.8)^2, (90-112.8)^2, (90-112.8)^2, (95-112.8)^2, (110-112.8)^2, (120-112.8)^2, (88-112.8)^2. Adding up those squared differences gives us 389.36. Then we divide 389.36 by 10 (the number of months) to get the variance of 38.936.
d. Standard Deviation: To find the standard deviation, we take the square root of the variance. Taking the square root of 38.936 gives us approximately 6.24.