Question

The water bill in X secondary school averages 120 with a standard deviation of 85. What percent have a water bill between 65 and 504, all expenses being in kwacha? (hint: use k = 2, 3 & 4)

a) Approximately 68%, 95%, and 99.7%
b) Approximately 95%, 99.7%, and 99.9%
c) Approximately 99.7%, 99.9%, and 99.99%
d) Approximately 68%, 99.7%, and 99.9%

Answer 1

The percentage of schools with a water bill between 65 and 504 kwacha approximately falls within three standard deviations of the mean, which, according to the empirical rule, is 99.7%.

Step-by-step explanation:

The question is regarding the percentage of schools with a water bill between 65 and 504 kwacha, given that the average water bill is 120 kwacha with a standard deviation of 85 kwacha. To determine this, we utilize the empirical rule (68-95-99.7 rule) which states that for a normal distribution, approximately 68% of data falls within one standard deviation of the mean, 95% within two standard deviations, and 99.7% within three standard deviations.

In this case, the values 65 and 504 are 0.647 and 4.517 standard deviations (respectively) from the mean. Therefore, we use k values of 1, 2, 3, and beyond. The school water bills within one standard deviation (k=1) would be 68%, within two standard deviations (k=2) would be 95%, and within three standard deviations (k=3) would be 99.7%. Since 504 is more than three standard deviations away from the mean, we can conclude that the percentage of schools with bills between 65 and 504 kwacha is approximately 99.7%.