Question

1. Assume that a random variable is normally distributed with a mean of µ = 50 and a standard deviation σ = 5, convert the following values to z scores:

1. X = 35
2. X = 40
3. X = 45
4. X = 50
5. X = 55
6. X = 60
7. X = 65

2. What is your observation about z values? Based on your observation how would you interpret z?

3. Sketch a graph for the standard normal distribution. Label the horizontal axis with your z values from question 1, describe the shape of this graph. What happens to the graph as z increases?

Answer 1

• The Z scores are:-

X-Values	Z-Scores
35
40
45
50
55
60
65

• Observation:- The Z scores are symmetric about zero.
• Interpretation : Z scores indicate how many standard deviation far the X is, from the mean (50).
• The standard normal graph is :-

• Description: The graph is bell shaped and symmetric about 0 .
• As Z increases, the height of the graph also increases upto 0. After 0, as Z increases , the graph starts to decrease anf after 3 the graph touches horizontal axis.