find the area under the standard distribution curve z=0 and z=0.98

Question

statistics question plz help me solve i dont understand and plz explain in steps

Answer 1

Madiha,

 

z-scores are standard scores and are used to indicate how many standard deviations a particular score is from the distribution's mean (average).

 

The Standard Normal Distribution (z-score distribution) looks like a normal distribution but in this case the mean of the z-score distribution is 0.

 

So, a z-score of 0 represents the mean (middle of the distribution graph).

 

A z-score of .98 (z-scores range from ~-4.0 to ~+4.0) lies to the right of the mean on the distribution almost 1 standard deviation away.  

 

The question asks what the area of the curve is between 0 and .98.  To find this, you need a z-score table (likely in your text or you can find one on-line).

 

The typical z-score table will tell you what the area is to the LEFT of the z-score.  So, in our case, the area to the left of .98 = .836 (that is, ~84% of the curve's area lies to the left of z = .98).

 

Now, the find the area between z = 0 and z = .98, we need to know that half the curve's area (.50) lies to the left of z = 0

 

Then, to find the area for 0 ≤ z ≤ .98, we subtract the area for z = 0 from z = .98:

 

.836 - .5 = .336 or ~34% of the curve's area lies between z = 0 and z =.98.

 

I hope this helps!