Download 3.13 Table A.

Bell Ringer
Mensa, the largest high-IQ society, accepts SAT
scores as indicating intelligence. Assume that
the mean combined SAT score is 1500, with
standard deviation 300. Jacinto scored a
combined 2070.
Maria took a traditional IQ test and scored
129. On that test, the mean is 100 and the
standard deviation is 15.
From the test scores, who is more intelligent?
Explain.
Daily Agenda
1.Review Bell Ringer
2.Section 3.7
3.Section 3.8
The extra step in finding cumulative proportions from a table is that
we must first standardize to express the problem in the standard
scale of z-scores.
This allows us to get by with just one table, a table of standard
Normal cumulative proportions.
Table A in the back of the book gives cumulative proportions for the
standard Normal distribution.
The pictures at the top of the table remind us that the entries are
cumulative proportions, areas under the curve to the left of a value z.
Examples 3.5 to 3.8 illustrated the use of software or Table A to find what
proportion of the observations satisfies some condition, such as “SAT
score above 820.”
We may instead want to find the observed value with a given proportion
of the observations above or below it.
Statistical software will do this directly.
3.13 Table A.
Use Table A to find the value z of a standard Normal variable that satisfies each
of the following conditions. (Use the value of z from Table A that comes closest to
satisfying the condition.) In each case, sketch a standard Normal curve with your
value of z marked on the axis.
(a)The point z with 65% of the observations falling below it
(b)The point z with 20% of the observations falling above it
3.14 The Medical College Admissions Test.
The total scores on the Medical College Admission Test (MCAT) in 2013 follow a
Normal distribution with mean 25.3 and standard deviation 6.5.
(a)What are the median and the first and third quartiles of the MCAT scores?
What is the interquartile range?
(b)Give the interval that contains the central 80% of the MCAT scores.