Questions: Using the standard Normal distribution tables, what is the area under the standard Normal curve corresponding to Z<0.95 ? 0.8289. 0.7500. 0.1711. 0.9599.

Using the standard Normal distribution tables, what is the area under the standard Normal curve corresponding to Z<0.95 ?

0.8289.
0.7500.
0.1711.
0.9599.

Transcript text: Question 13 2 pts Using the standard Normal distribution tables, what is the area under the standard Normal curve corresponding to $Z<0.95$ ? 0.8289. 0.7500. 0.1711. 0.9599.

Solution

Solution Steps

Step 1: Define the Problem

We need to find the area under the standard Normal curve corresponding to $ Z < 0.95 $. This can be expressed mathematically as:

\[ P(Z < 0.95) = \Phi(0.95) - \Phi(-\infty) \]

where $ \Phi(z) $ is the cumulative distribution function (CDF) of the standard normal distribution.

Step 2: Calculate the CDF Values

For the standard normal distribution, we know that:

\[ \Phi(-\infty) = 0 \]

Thus, the equation simplifies to:

\[ P(Z < 0.95) = \Phi(0.95) - 0 = \Phi(0.95) \]

Step 3: Find $ \Phi(0.95) $

Using the standard normal distribution tables or a statistical function, we find:

\[ \Phi(0.95) = 0.8289 \]

Final Answer

The area under the standard Normal curve corresponding to $ Z < 0.95 $ is

\[ \boxed{0.8289} \]

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