## STAT XL 10

Introduction to Statistical Reasoning

## Instructor: Ivo Dinov, Asst. Prof.

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

Due Date:

# Wednesday, May 01, 2002, turn in after lecture

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

• (HW_2_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. What is the chance that a randomly selected English word has 2 character-length?
•  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_2_2) Suppose that X~Normal(m =3, sd=4) compute the Z-scores for the following numbers and state how many SD's is each of these numbers aways from m:
• -5
• 11
• 5
• 1.4
• What is the probability P(-3<X<-1)?

• (HW_2_3) Suppose the Stat XL 10 midterm exam scores in the Spring 2002 had a mean of 85 and a standard deviation of 15. Suppose X represents a random exam score. Standardize X and compute how likely is that 75<X<98, assuming exam scores can be modeled well by a (general) Normal distribution.

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