Part 2: you are given an area (=probability), and

Questions: Part 2: you are given an area (=probability), and you need to compute c, which is the z-score that corresponds to the statement: P(-c<z<c)=0.5 (This is an inverse standard normal distribution problem. Use technology to compute c) The arrow can only be dragged to tick marks that are multiples of 0.1 So, round c to 1 decimal place, and then move the arrow to that rounded value. Click on the "Shade" menu to select the shading option corresponding to the question (to the left, to the right, or between 2 values). (If the question is less c, choose Left of a value. If it greater than c, choose right of a value.) Then slide the arrow to the round value of c. Shade: Left of a value. Click and drag the arrows to adjust the values.

Transcript text: (b) Part 2: you are given an area (=probability), and you need to compute c, which is the z-score that corresponds to the statement: \[ P(-c

Solution

Solution Steps

Step 1: Understand the Problem

We need to find the z-score \( c \) such that the probability \( P(-c < z < c) = 0.5 \) for a standard normal distribution.

Step 2: Identify the Symmetry

Since the standard normal distribution is symmetric around 0, the probability \( P(-c < z < c) = 0.5 \) implies that the area in each tail is \( (1 - 0.5) / 2 = 0.25 \).

Step 3: Use the Standard Normal Distribution Table

We need to find the z-score that corresponds to a cumulative probability of 0.75 (since 0.5 + 0.25 = 0.75).

Step 4: Find the Z-Score

Using the standard normal distribution table or a calculator, we find that the z-score corresponding to a cumulative probability of 0.75 is approximately 0.674.