Download 1/9 z-score Table Practice Packet

FST
Z-scores on a Normal Curve
1/9/17
Quick Refresher- Draw a normal curve and mark ±1, ±2, ±3 standard deviations. Today we will use a
normal curve to look at percentages that are not so convenient.
Issue – How to find percentages for data not at multiples of standard deviations.
IF the data is normally distributed then we can use z scores to find the percent of data below a given
score.
Example: The length of math textbooks is normally distributed with a mean of 753 pages and a
standard deviation of 34 pages.
a) What percent of textbooks are below 700 pages?
b) What percent of textbooks would be between 700 pages and 775 pages?
c) What percent of textbooks would be greater than 850 pages?
d) How many pages would a book need to have in order to be longer than 90% of the math textbooks?
IF you have the data you can decide if a distribution is normally distributed.
Use the normal probability plot to analyze the data’s normality.
FST
HW for Normal Z
Name: ________________________
1. The cholesterol levels of adult women can be normally approximated with a mean of 188
mg/dL and a standard deviation of 24 mg/dL.
a) Draw a normal curve for this distribution, marking out ±1, 2, & 3 standard deviation values
from the mean.
b) What percent of women would have a cholesterol level above 200?
c) What percent of women would be between 150 & 170?
d) What is a good estimate for the IQR of the data?
e) Above what level is the highest 15% of women?
2. Goodyear claims that tread life on its tires is normally distributed and has a mean of 32,000
miles and a standard deviation of 2,500 miles.
a) Would it be reasonable to think that a tire could last at least 40,000 miles? Give justification for
your decision.
b) What percent of tires will not last past 30,000 miles?
c) If they have to refund the purchase price for any tire that lasts in the bottom 4% of tread life,
how many miles would be the top of that interval?
3. Plastico Inc. makes chairs for Kindergarten rooms and needs to try and match their chairs to
the size of students. Their research indicates that kindergartners’ heights are normally
distributed with a mean of 38.62 in. and a s. dev. of 1.8 in.
a) What percent of kindergartners would be less than 3 feet tall?
b) If Plastico Inc. wants to accommodate the middle 80% of students, what heights should they
build their chairs for?
4. The times for men’s downhill scores are listed below. If you used your own TI-Nspire in class
today, the data is on page 2.1 of the document from class.
a) Is the data normally distributed?
b) If it is, what is the percent of the data that should be less than 109.78? What percent actually
is less?
c) Is there a difference? Can you explain it if there is?