Question

Describe the standard normal curve.

a. What does the mean, median, and mode equal?

1. How many standard deviations are on the right side of the curve?

2. How many standard deviations are on the left side of the curve?

3. What does the y-axis represent?

4. Draw the standard normal curve.

Answer 1

Q1)A standard normal curve is a special case of a normal curve when the mean = 0 and standard deviation = 1

It is a bell shaped curve, just like the normal curve. It is Unimodal in nature.

The area under the curve = 1.

Q2) For the standard normal curve, Mean = Median = Mode = 0

This is because the graph of standard normal curve is syymetrical and the mean divides the graph into 2 equal halves, hence there is equal sets of values on either side of the mean, hence Mean = Median. The graph is also unimodal, and it is achieved at Mean = 0. Hence Mean = Median = Mode = 0.

Q3&4) There is 3 standard deviations on the right and left side of the mean in the standard normal curve. The third standard deviation on either side, together, cover 99.7% of the area under the curve.

Q5) Y axis represents the value of prabability density function, plotted against different values of x.

Q6)