Final answer:
a. The mean monthly charge is $600 and the standard deviation is $330.62. b. The probability that a person charges less than $200 per month is 11.12%. c. The probability that a person charges more than $900 per month is 81.86%. d. 80.78% of monthly charges are between $600 and $889.
Step-by-step explanation:
a. To find the mean monthly charge, we need to find the average of the minimum ($100) and maximum ($1,100) charges. The mean is calculated by adding the two values and dividing by 2: ($100 + $1,100) / 2 = $600. The standard deviation can be found using the formula: stdDev = (max - min) / sqrt(12) = ($1,100 - $100) / sqrt(12) = $330.62.
b. To find the probability that a person charges less than $200 per month, we need to calculate the z-score using the formula: z = (x - mean) / stdDev = ($200 - $600) / $330.62 = -1.21. From the z-table, we find that the probability corresponding to a z-score of -1.21 is 0.1112 or 11.12%.
c. To find the probability that a person charges more than $900 per month, we use the same steps as in part b, but with the value of $900. The z-score is (900 - 600) / 330.62 = 0.91. From the z-table, the probability corresponding to a z-score of 0.91 is 0.8186 or 81.86%.
d. To find the percent of monthly charges between $600 and $889, we first calculate the z-scores for both values: z1 = (600 - 600) / 330.62 = 0 and z2 = (889 - 600) / 330.62 = 0.87. From the z-table, we find the probability corresponding to a z-score of 0.87 is 0.8078 or 80.78%. Since the uniform distribution is continuous, the probability of the charges falling between $600 and $889 is given by: 0.8078 - 0 = 0.8078 or 80.78%.