Math225 Week 5 Assignment: Understanding Normal Distribution Questions

**Question**

Suppose X∼N(18,2), and x=22. Find and interpret the z-score of the standardized normal random variable.

**Question**

The graph below shows the graphs of several normal distributions, labeled A, B, and C, on the same axis. Determine which normal distribution has the smallest mean.

**Question**

Given the plot of normal distributions A and B below, which of the following statements is true? Select all correct answers.

**Question**

Suppose X∼N(12.5,1.5), and x=11. Find and interpret the z-score of the standardized normal random variable.

**Question**

Given the plot of normal distributions A and B below, which of the following statements is true? Select all correct answers.

**Question**

Given the plot of normal distributions A and B below, which of the following statements is true? Select all correct answers.

**Question**

Rosetta averages 148 points per bowling game with a standard deviation of 14 points. Suppose Rosetta’s points per bowling game are normally distributed. Let X= the number of points per bowling game. Then X∼N(148,14).

If necessary, round to three decimal places.

**Question**

Suppose X∼N(16.5,0.5), and x=16. Find and interpret the z-score of the standardized normal random variable.

# Solution:

Suppose X∼N(18,2), and x=22. Find and interpret the z-score of the standardized normal random variable.

**Answer**: The z-score when x=22 is 2. The mean is 18.

This z-score tells you that x=22 is 2 standard deviations to the** right** of the mean.

The graph below shows the graphs of several normal distributions, labeled A, B, and C, on the same axis. Determine which normal distribution has the smallest mean…**Please click the icon below to download at $5**