Ch 11 - Bayes' theorem & Normal Distribution

Question 1

Normal—or Gaussian—distributions are

Answer 1

a family of symmetrical, bell-shaped density curves defined by a mean m (mu) and a standard deviation s (sigma): N(m,s).

Question 2

Normal distrabution inflection point

Answer 2

Question 3

Normal curves are used to

Answer 3

model many biological variables. They can describe a population distribution or a probability distribution .

Question 4

Normal Curve means vs SD

Answer 4

Question 5

Good candidate for a normal model

Answer 5

Question 6

All normal curves N(µ,σ) share the same properties

Answer 6

About 68% of all observations are within 1 standard deviation (s) of the mean (m).

About 95% of all observations are within 2 s of the mean m.

Almost all (99.7%) observations are within 3 s of the mean.

Question 7

What % have low or very low

Answer 7

Question 8

Answer 8

Question 9

We can standardize data by

Answer 9

computing a z-score

Question 10

A z-score measures

Answer 10

the number of standard deviations that a data value x is from the mean m.

Question 11

When x is 1 standard deviation larger than the mean, then z =

Answer 11

Question 12

When x is 2 standard deviations larger than the mean, then z =

Answer 12

Question 13

When x is larger than the mean, z is

Answer 13

positive.

Question 14

When x is smaller than the mean, z is

Answer 14

negative.

Question 15

Answer 15

Question 16

Table B gives

Answer 16

the area under the standard Normal curve to the left of any z-value.

Question 17

two ways of finding the area under N(0,1) curve to the right of a z-value.

Answer 17

Question 18

To calculate the area between two z-values

Answer 18

first get the area under N(0,1) to the left for each z-value from Table B.

Then subtract the smaller area from the larger area.

Don’t subtract the z-values!!! Normal curves are not square!

Question 19

he area under N(0,1) for a single value of z is

Answer 19

zero
because area under a point is a line which is zero

(need a range)

Question 20

Answer 20

Question 21

Inverse normal calculations
find probability from z score

Answer 21

Question 22

The lengths of pregnancies, when malnourished mothers are given vitamins and better food, is approximately N(266, 15). How long are the 75% longest pregnancies in this population?

Answer 22

Question 23

way to assess if a data set has an approximately Normal distribution is to

Answer 23

plot the data on a Normal quantile plot.

Cannot do by hand - use technology

1) The data points are ranked and the percentile ranks are converted to z-scores.
2) The z-scores are then used for the horizontal axis and the actual data values are used for the vertical axis.
3) If the data have approximately a Normal distribution, the Normal quantile plot will have roughly a straight-line pattern.