Class Activity #3

Given a normal distribution with μ = 36 and σ = 3.4, find the following:

1. Find and sketch the area under the normal curve for the following conditions:
   1. x > 41.8.
   2. x < 38.1.
   3. 35.6 < x < 37.9.
2. Find and sketch the area under the normal curve for the following conditions:
   1. z > –0.3.
   2. z < –1.7.
   3. –0.8 < z < 1.2.
3. Why is the standard normal distribution needed/used?
4. For what value of x is 57% of the area under the normal curve to the right? Sketch the area.
5. For what value of z is 32% of the area under the normal curve to the left? Sketch the area.

ANSWERS:

1. The area under the normal curve is found by using NDAREA program on TI-83 calculator:
   1. 
   2. 
   3. 
2. The area under the normal curve is found by using NDAREA program on TI-83 calculator:
   1. 
   2. 
   3. 
3. The standard normal distribution is used to compare all normal distributions.
4. Use invNorm() function on TI-83. invNorm(0.43, 0, 1) = –0.176.
   The graph is:
5. Use invNorm() function on TI-83. invNorm(0.32, 0, 1) = –0.468.
   The graph is: