## STAT 10

(Sec. 3a-3c)

Introduction to Statistical Reasoning

## Instructor: Ivo Dinov, Asst. Prof.

Departments of Statistics & Neurology
 http://www.stat.ucla.edu/~dinov/

Due Date:

# Friday, Oct.19, 2001, turn in after lecture

See the HW submission rules. On the front page include the following header.

• (HW_3_1) The following table represents the lengths, in terms of number of characters,  of 100 English words randomly chosen from a dictionary. Construct the frequency table and compute the average length of an English word using two ways (the raw data and the frequency of occurrence). Calculate the standard deviation of the word lengths from the mean. Using these estimates draw the histogram representing the data distribution.
•  3 2 2 4 4 4 3 9 9 3 6 2 3 2 3 4 6 5 3 4 2 3 4 5 2 9 5 8 3 2 4 5 2 4 1 4 2 5 2 5 3 6 9 6 3 2 3 4 4 4 2 2 4 2 3 7 4 2 6 4 2 5 9 2 3 7 11 2 3 6 4 4 7 6 6 10 4 3 5 7 7 7 5 10 3 2 3 9 4 5 5 4 4 3 5 2 5 2 4 2

• (HW_3_2) Suppose that X~ Normal(m=3, s=4) compute the corresponding standard Z-scores for the following numbers, state how many SD's is each of these numbers aways from m, and calculate the area under the distribution curve on the given interval:
• -5, [-5 : 5]
• 11, [-infinity : 11]
• 5, [5 : infinity]
• 1.4, [0 : 1.4]
• What is the probability P(-3<X<-1)? Is it different from P(-3<=X<=-1)? Why?

\Ivo D. Dinov, Ph.D., Departments of Statistics and Neurology, UCLA School of Medicine/