Download Reading Standard Normal Distribution Table

Probability and Statistics – Mrs. Leahy
Chapter 5 Test Study Guide:
Key Features of Normal Curve:



Symmetrical About the Mean
Bell Shaped
Curve approaches, but never touches the x axis
Reading Standard Normal Distribution Table:
z score tells the number of standard deviations that x is from the mean.
Standard Normal Distribution Table:
Tells you the probability that a raw score x falls to the left of a specified z value.
1. P( z  1.38)
2. P( z  0.45)
Standard Normal Distribution Table:
Use a given probability to estimate a z-score.
3. P(1.25  z  1.78)
If probabilty not on table, choose closest probability.
If exactly between 2 probabilities, average their z-scores.
4. Find z such that 8% of the standard normal curve lies to the left of z.
5. Find z such that 42% of the standard normal curve lies to the right of z.
Formulas in this Chapter:
x
standard score:
z
convert standard score to raw score:
x  z  
convert mean to standard score:
z

x

n
What does “Unusual” Mean?
Areas Under ANY Normal Curve
6. P( x  95);   80;  25
7. P( x  115);   80;  25
8. P(60  x  75);   80;  25
Find x if you know the probability
9. The average life of a refrigerator is 14 years with a standard
deviation of 2.5 years. A company has a guarantee program that
will replace the product if it breaks. How many years (round to
nearest tenth) should they guarantee the product if they don’t
want to replace more than 5% of the refrigerators?
Central Limit Theorem
Ex. In mountain country, major highways sometimes use tunnels instead of long, winding roads over high passes.
However, too many vehicles in the tunnel at the same time can cause a hazardous situation. Traffic engineers are
studying a long tunnel in Colorado. If x represents the tme for a vehicle to go through the tunnel, it is known that
the x distribution has a mean of 12.1 minutes and a standard deviation of 3.8 minutes under normal traffic
conditions. The shape of the x distribution is mound shaped symmetrical.
Engineers have calculated that on average, vehicles should spend from 11 to 13 minutes in the tunnel -- less than
11 minutes means traffic is moving too fast, more than 13 minutes creates a problem of bad air quality.
10) If a sample of 50 vehicles is selected, what is the probability that the mean time for the 50 vehicles will be less
than 10 minutes?
11.) If a sample of 50 vehicles is selected, what is the probability that the mean time for the 50 vehicles will be
from 11 to 13 minutes?