0 0.89 201 Use the TI-84 calculator to find the area of the shaded region.

0 0.89 201 Use the TI-84 calculator to find the area of the shaded region.

The Correct Answer and Explanation is:

To find the area of the shaded region on a TI-84 calculator, based on the input “0 0.89 201,” we assume that:

• The lower bound of integration is 0
• The upper bound of integration is 0.89
• The function is the standard normal distribution, where 201 refers to the normal cumulative area (z = 0.89)

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✅ Correct Answer:

Using the TI-84:

1. Press 2nd then VARS to access the DISTR menu.
2. Choose option 2:normalcdf(
3. Enter the values: scssCopyEditnormalcdf(0, 0.89, 0, 1) This inputs:
   • Lower bound = 0
   • Upper bound = 0.89
   • Mean = 0 (standard normal)
   • Standard deviation = 1
4. Press ENTER

📌 Result:

scssCopyEditnormalcdf(0, 0.89, 0, 1) ≈ 0.3133

✅ Final Answer:

The area of the shaded region is approximately 0.3133

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📘 Textbook-Style Explanation

In statistics and probability, the area under a normal curve represents the probability or proportion of values falling within a certain range. The standard normal distribution has a mean (μ) of 0 and a standard deviation (σ) of 1. This question asks for the area under the standard normal curve from z = 0 to z = 0.89.

To calculate this on a TI-84 calculator, we use the normalcdf (cumulative distribution function), which computes the area under the normal curve between two z-values. The syntax is:

luaCopyEditnormalcdf(lower bound, upper bound, μ, σ)

Since this is a standard normal curve, μ = 0 and σ = 1. We input:

scssCopyEditnormalcdf(0, 0.89, 0, 1)

This command instructs the calculator to find the area from z = 0 to z = 0.89. Pressing ENTER returns approximately 0.3133, meaning that about 31.33% of the data falls between these two z-values.

This shaded region often represents a probability or proportion in a real-world context. For example, if scores on a test are normally distributed, 31.33% of students scored between the mean and 0.89 standard deviations above the mean.

Using graphing calculators like the TI-84 simplifies statistical analysis by providing accurate results without needing tables or complex formulas.