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Electricity Bills:

According to a government energy agency, the mean monthly household electricity bill in the United States in 2011 was [tex]\$109.72[/tex]. Assume the amounts are normally distributed with a standard deviation of [tex]\$17.00[/tex]. Use the TI-84 Plus calculator to answer the following:

(a) Find the 7th percentile of the bill amounts.
(b) Find the 64th percentile of the bill amounts.
(c) Find the median of the bill amounts.

Round the answers to at least two decimal places.

Part 1 of 3
The 7th percentile of the bill amounts is [tex]\$ \square[/tex].

Part 2 of 3
The 64th percentile of the bill amounts is [tex]\$ \square[/tex].

Part 3 of 3
The median of the bill amounts is [tex]\$ \square[/tex].

Sagot :

GinnyAnsweridn
Let's solve this step-by-step while elaborating on each part of the question in detail.

Given:
- The mean monthly household electricity bill in the United States in 2011: \[tex]$109.72 - Standard deviation: \$[/tex]17.00

We need to find the following:
(a) The 7th percentile of the bill amounts.
(b) The 64th percentile of the bill amounts.
(c) The median of the bill amounts.

### Part 1: The 7th percentile of the bill amounts

To find the 7th percentile, we need to determine the point at which 7% of the values lie below it in a normal distribution with the given mean and standard deviation.

The value corresponding to the 7th percentile is found to be approximately:
[tex]\[ \$84.63 \][/tex]

### Part 2: The 64th percentile of the bill amounts

To find the 64th percentile, we need to determine the point at which 64% of the values lie below it in the normal distribution with the given mean and standard deviation.

The value corresponding to the 64th percentile is:
[tex]\[ \$115.81 \][/tex]

### Part 3: The median of the bill amounts

In a normal distribution, the median is the same as the mean. Therefore, the median of the bill amounts is:
[tex]\[ \$109.72 \][/tex]

### Summary of Answers:
(a) The 7th percentile of the bill amounts is: \[tex]$84.63 (b) The 64th percentile of the bill amounts is: \$[/tex]115.81
(c) The median of the bill amounts is: \$109.72

By carefully assessing each part and utilizing the properties of the normal distribution, we have determined the required percentiles and the median.
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