Download Chap 3 Lesson 5 filled in - Spring

Prob/Stat
Name: _______________________
Date: _____________ Period: ____
Chapter 3 – Section 5 – Finding a Specific Data Value
You can use the normal distribution to find a specific data value (an x-value) for a given
probability. InvNorm on the calculator will give you the z-score for a given area (to the left)
1. Draw a picture!
Note: invnorm(area to left) = z
2. Take the percent from problem and write it as a LEFT/LOWER problem decimal.
* If less than (picture shaded to left), keep decimal value as is.
* If greater than (picture shaded to right), subtract % from 100 or decimal
from 1 (1 – decimal) or (100 - %)
3. Use the calculator: w/older calculators: 2nd Vars #3: InvNorm(% as decimal) = z
w/newer calculators: area: decimal value to the left (found in step 2) = z
 0
 1
4. Use the formula for changing a z-score to an x-value: x  z  
Examples – Draw pictures for each!!!!
1. Scores for a civil service exam are normally distributed with a mean of 75 and a standard
deviation of 6.5. To be eligible for civil service employment, you must score in the top 5%.
What is the lowest score you can earn and still be eligible for employment?
2. The length of time employees have worked at a corporation is normally distributed, with a
mean of 11.2 years and a standard deviation of 2.1 years. In a company cutback, the lowest 10%
in seniority are laid off. What is the maximum length of time an employee could have worked
and still be laid off?
3. A survey was conducted to measure the height of American males. In the survey, respondents
were grouped by age. In the 20-29 age group, the heights were normally distributed, with a
mean of 69.2 inches and a standard deviation of 2.9 inches.
Picture:
What height represents the first quartile?
What height represents the 90th percentile?
HW: WS Problems (Attached). Read p. 81 – 85
3.5 HW – Finding Specific Data Values Homework Problems
1. Assume the cholesterol levels of adult American women can be described by a Normal model
with a mean of 188 mg/dL and a standard deviation of 24.
Picture:
a. Above what value are the highest 15% of women’s cholesterol levels?
b. What is the first quartile of the distribution of women’s cholesterol?
2. Companies who design furniture for elementary school classrooms produce a variety of sizes
for kids of different ages. Suppose the heights of kindergarten children can be described by a
Normal model with a mean of 38.2 inches and standard deviation of 1.8 inches.
Picture:
a. At least how tall are the biggest 10% of kindergarteners?
b. At most how tall are the smallest 10% of kindergarteners?
3. The annual per capita consumption of oranges in the US can be approximated by the normal
distribution with a mean of 14.9 pounds and a standard deviation of 3 pounds.
Picture:
a. What annual per capita consumption of oranges represents the 5th percentile?
b. What annual per capita consumption of oranges represents the third quartile?
4. The time spent waiting for a heart transplant in Ohio and Michigan for patients with type A+
blood can be approximated by a normal distribution with a mean of 127 days and a standard
deviation of 23.5 days.
Picture:
a. What is the shortest time spent waiting for a heart that would still place a patient in
the top 30% of waiting times?
b. What is the longest time spent waiting for a heart that would still place a patient in
the bottom 10% of waiting times?