Ivo Dinov
UCLA Statistics, Neurology, LONI
, Math/PIC
 Courses SOCR Ivo Dinov's Home SiteMap Software Contact

STAT 13 (1a, 1b, 1c, 1d)

Introduction to Statistical Methods for the Life and Health Science

Department of Statistics

## Instructor: Ivo Dinov

Homework 4
Due Date: Wednesday, Feb. 09, 2011

Please, submit your homework before lecture on the due date. See the HW submission rules. On the front page include the following header.
• (HW_4) Do the following problems using the interactive SOCR Normal Distribution calculator. Include snapshots of all of your work to support your findings.

• The brain weights of adult Swedish males are approximately normally distributed with mean μ = 1,300g and standard deviation 90g. Let Y denote the brain weight of a randomly chosen person from this population. Calculate:
• P(Y <=1,390).
• P(1,325 <= Y <=1,425).
• P(1,350 <= Y).
• P(1,400 <= Y).
• P(1,400 <= Y <=1,500).
• P(1,300 <=Y <=1,350).

• The serum cholesterol levels of 17-year-olds follows a normal distribution with mean 176 mg/dLi and standard deviation 30 mg/dLi. What percentage of 17-year-olds have serum cholesterol values:
• 176 or less?
• 168 or more?
• 210 or less?
• 130 or more?
• between 176 and 206?
• between 123 and 157?
• between 155 and 186?

• Using the Hotdogs Dataset, create separate normal probability plots of the calories and sodium variables. Do you consider either of these variables to be Normally distributed? Do the distributions of these 2 variables appear similar?

• The litter size of a certain population of female mice follows approximately a normal distribution with mean 7.8 and standard deviation 2.0. Let Y be the size of a randomly chosen litter. Use the Normal Distribution calculator to find approximate values for these probabilities:
• P(Y <= 7)
• P(Y = 7)
• P(6 <= Y <= 11)

• A survey of mitochondrial DNA variation in smelts in a lake revealed that 2 haplotypes (genotypes) were present in the population. 30% of the fish were of haplotype A, and the remaining 70% were haplotype B. If we sample 400 fish from the lake, what is the probability that:
• at least 130 are haplotype A?
• at least 300 are haplotype B?
• Between 115 and 145 are haplotype A?
• 160 or more are haplotype A?
• Simulate these experiments using the SOCR Binomial Coin Experiment. Compare your exact calculations with the results of your simulations.

• Resting heart rate was measured for a group of subjects; then the subjects drank 6 ounces of coffee. Ten minutes later their heart rates were measured again. The change in heart rate followed a normal distribution, with mean increase of 6.9 beats per minute and a standard deviation of 9.8. Let Y denote the change in heart rate for a randomly selected person. Find:
• P(Y > 9).
• P(Y > 19).
• P(6 < Y < 14).

 Ivo Dinov's Home http://www.stat.ucla.edu/~dinov Visitor number, since Jan. 01, 2002 I.D.Dinov 1997-2011