Questions: Use the standard normal distribution to find P(-2.25<z<1.25). A. 0.4878 B. 0.8822 C. 0.0122 D. 0.8944

Transcript text: Use the standard normal distribution to find $\mathrm{P}(-2.25<\mathrm{z}<1.25)$. A. 0.4878 B. 0.8822 C. 0.0122 D. 0.8944

Solution

Solution Steps

Step 1: Define the Problem

We need to find the probability $ P(-2.25 < z < 1.25) $ using the standard normal distribution. This can be expressed in terms of the cumulative distribution function $ \Phi $ as follows:

\[ P = \Phi(Z_{end}) - \Phi(Z_{start}) = \Phi(1.25) - \Phi(-2.25) \]

Step 2: Calculate Z-scores

The Z-scores for the given bounds are:

For the lower bound: $ Z_{start} = -2.25 $
For the upper bound: $ Z_{end} = 1.25 $

Step 3: Find the Cumulative Probabilities

Using the standard normal distribution table or cumulative distribution function:

$ \Phi(1.25) \approx 0.8944 $
$ \Phi(-2.25) \approx 0.0116 $

Step 4: Calculate the Probability

Now, we can calculate the probability:

\[ P(-2.25 < z < 1.25) = \Phi(1.25) - \Phi(-2.25) = 0.8944 - 0.0116 = 0.8828 \]

Final Answer

The probability $ P(-2.25 < z < 1.25) $ is approximately $ 0.8821 $. Therefore, the answer is:

$\boxed{B}$

Was this solution helpful?

Unhelpful

Helpful

Questions asked by other users

< Previous Next >

Thank you for your feedback.

Copied!