## STAT 110A

(Sec. 3)

Applied Statistics

## Instructor: Ivo Dinov, Asst. Prof.

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

Due Date:

# Friday, May 03, 2002, turn in after lecture

Please, turn in your homework on the due date. See the HW submission rules. On the front page include the following header.

• (HW_3_1) Suppose X ~ Normal(m = 23, s = 2). The following table of probabilities was obtained from Excel.
 x P(X<=x) x P(X<=x) x P(X<=x) 15 0.0000 20 0.0668 25 0.8413 16 0.0002 21 0.1587 26 0.9332 17 0.0013 22 0.3085 27 0.9772 18 0.0062 23 0.5000 28 0.9938 19 0.0228 24 0.6915 29 0.9987

Compute the following probabilities:
(i ) pr(X <= 19);   (ii) pr(X < 19);  (iii) pr(X > 21);
(iv) pr(24 <= X <= 27)

• (HW_3_2) The number of liters of soft serve ice cream sold by an ice cream van driver a day is found to be Normally distributed with a mean of 8.6 liters and a standard deviation of 1.28 liters. The following table of probabilities was obtained from STATA:
 P(X<=x) x 0.1000 6.9596 0.2500 7.7367 0.7500 9.4633 0.9000 10.2404

(i) What is the least amount of soft serve ice cream that is needed so that the driver can satisfy demand on 90% of afternoons?

(ii) What is the inter quartile range for the ice cream sales.

(iii) What is the probability that X is greater than 6?

• (HW_3_3) X has a mean of -3 and a standard deviation of 5 and W has a mean of 5 and a standard deviation of 3. Let X and W be independent Normal random variables and let Y = 3X - 3W.

(i) What are the mean and standard deviation of Y?

(ii) What can we say about the shape of the distribution of Y?

• (HW_3_4) Use Poisson approximation to Binomial distribution to answer the following question:
The performance of a communication network is seriously degraded if more than 0.001% of the transferred bits (0's & 1's) are incorrectly decoded (received). The probability that a single bit is corrupted during transmission is 2x10-5 and that chance that any particular bit is incorrectly  transmitted is independent of any other bits. Approximately what is the probability that a message of 105 bits is  seriously degraded?

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