Question

The monthly utility bills in a city are normally distributed with a mean of $100 and a standard deviation of $16 find the probability that a randomly selected utility bill is

(A) less than $67
(B) between $82 and $100
(C) more than $120​

Answer 1

To find the probabilities, we use z-scores and the standard normal distribution table. For each scenario, we calculate the z-scores and look them up in the table to find the corresponding probabilities. The probabilities are approximately 0.019, 0.130, and 0.894 for (A), (B), and (C) respectively.

Step-by-step explanation:

To find the probability, we need to use z-scores and the standard normal distribution table.

(A) To find the probability that a randomly selected utility bill is less than $67, we need to find the z-score. z = (x - mean) / standard deviation = (67 - 100) / 16 = -33/16 = -2.06. Looking up this value in the standard normal distribution table, we find the probability to be approximately 0.019.

(B) To find the probability that a randomly selected utility bill is between $82 and $100, we need to find the z-scores for each value. z1 = (82 - 100) / 16 = -18/16 = -1.13 and z2 = (100 - 100) / 16 = 0. Looking up these values in the standard normal distribution table, we find the probability to be approximately 0.130.

(C) To find the probability that a randomly selected utility bill is more than $120, we need to find the z-score. z = (120 - 100) / 16 = 20/16 = 1.25. Looking up this value in the standard normal distribution table, we find the probability to be approximately 0.894.