Questions: Consider the following interval. the area between (z=1.43) and (z=2.15) Sketch the area under the standard normal curve over the indicated interval and find the specified area. (Round your answer to four decimal places.)

Consider the following interval.
the area between (z=1.43) and (z=2.15)

Sketch the area under the standard normal curve over the indicated interval and find the specified area. (Round your answer to four decimal places.)
Transcript text: Consider the following interval. the area between $z=1.43$ and $z=2.15$ Sketch the area under the standard normal curve over the indicated interval and find the specified area. (Round your answer to four decimal places.)
failed

Solution

failed
failed

Solution Steps

Step 1: Identify the Problem

We need to find the area under the standard normal curve between \( z = 1.43 \) and \( z = 2.15 \).

Step 2: Use the Standard Normal Distribution

The area under the standard normal curve between two z-values can be found using the cumulative distribution function (CDF) for the standard normal distribution.

Step 3: Calculate the Area

The area between \( z = 1.43 \) and \( z = 2.15 \) is given by: \[ \text{Area} = \Phi(2.15) - \Phi(1.43) \] where \(\Phi(z)\) is the CDF of the standard normal distribution.

Using standard normal distribution tables or a calculator: \[ \Phi(2.15) \approx 0.9842 \] \[ \Phi(1.43) \approx 0.9236 \]

Thus, the area is: \[ \text{Area} = 0.9842 - 0.9236 = 0.0606 \]

Final Answer

The area under the standard normal curve between \( z = 1.43 \) and \( z = 2.15 \) is approximately 0.0606.

{"axisType": 3, "coordSystem": {"xmin": -3, "xmax": 3, "ymin": -0.1, "ymax": 0.5}, "commands": ["y = exp(-0.5_x**2)/sqrt(2_pi)"], "latex_expressions": ["$y = \\frac{1}{\\sqrt{2\\pi}} e^{-\\frac{x^2}{2}}$"]}

Was this solution helpful?
failed
Unhelpful
failed
Helpful