Electricity bills: According to a government energy agency, the mean monthly household electricity bill in the United States in 2011 was $108.99. Assume the amounts are normally distributed with standard deviation $19.00. Use the TI-84 Plus calculator to answer the following. The probability that a randomly selected household had a monthly bill less than $119 is __

To calculate the probability that a randomly selected household had a monthly bill less than $119, we need to use the **normal distribution** formula. Specifically, we need to compute the **cumulative probability** up to $119 using the given mean and standard deviation.

The **parameters** of the normal distribution are:
- Mean ($\mu$) = 108.99
- Standard deviation ($\sigma$) = 19.00

The goal is to find $P(X < 119)$.

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### Step-by-Step Guide for TI-84 Plus:

1. **Access the normal distribution function**:  
   Press `2nd` → `VARS` to open the `DISTR` menu.  
   Select **2:normalcdf(**

2. **Enter the parameters**:  
   - Lower bound: $-10^9$ (Use a very small number to represent $-\infty$)
   - Upper bound: 119 (the value we are interested in)
   - Mean: 108.99
   - Standard deviation: 19.00  

   So you will input:  
   `normalcdf(-10^9, 119, 108.99, 19)`

3. **Press Enter**:  
   The calculator will return the probability value.

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### Solution:

If you follow the steps on the TI-84 Plus, you should get:

\[
P(X < 119) \approx 0.7664
\]

This means there is approximately a **76.64% chance** that a randomly selected household had a monthly bill less than $119.

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Would you like a detailed breakdown of the calculation process? 

Here are some related questions for deeper understanding:

1. What is the probability of a bill being greater than $130?
2. How do you find the z-score for a given value in a normal distribution?
3. What does the standard deviation represent in this problem?
4. How would the result change if the standard deviation were larger or smaller?
5. How do you use the **z-table** for these kinds of probability questions?

**Tip**: Always sketch a normal curve with the mean and relevant points marked to help visualize probabilities.

According to a government energy agency, the mean monthly household electricity bill in the United States in 2011 was $108.99. Assume the amounts are normally distributed with standard deviation $19.00. Use the TI-84 Plus calculator to answer the following: The probability that a randomly selected household had a monthly bill less than $119 is __

Learn to calculate the probability of a monthly household electricity bill being less than $119 given a mean of $108.99 and a standard deviation of $19.00 using the TI-84 Plus. This problem involves the normal distribution and cumulative probability function, suitable for Grades 10-12.

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