|STAT 13 (1a,
1b, 1c, 1d)
Methods for the Life and Health Science
|Department of Statistics
Instructor: Ivo Dinov
|Due Date: Wednesday, Feb. 15, 2012
- (HW.4.1) There is
interest in comparing different countries in the World based on variety
of factors reflecting the country's internal and external international
ranking. Use the
Political, Economic, Health, and Quality-of-Life Data of the 100
Countries to estimate the probabilities below. Let ED=Economic
Dynamism of a Country, which is an index of productive growth in US
dollars. Use the SOCR
Modeler to fit a Normal Distribution Model to the ED variable
(column) in this
dataset (see this Help
Onces you obtain estimates for the mean and standard deviation of the
normal model (see the Results tab in the
Modeler) use the SOCR
Normal Distribution Calculator to estimate
the likelihoods of these events:
- P(ED <=45).
- P(35 <= ED <=41).
- P(47 <= ED).
- P(59 <= ED).
- P(46 <= ED <=87).
- P(20 <= ED <=57).
- (HW.4.2) 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?
- (HW.4.3) Using the
Dataset, create separate normal
probability plots of the calories
variables. Do you consider either of these variables to be Normally
distributed? Do the distributions of these 2 variables appear similar?
- (HW.4.4) The
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
- P(Y <= 7)
- P(Y = 7)
- P(6 <= Y <= 11)
- (HW.4.5) A survey
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
- 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.
- (HW.4.6) 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).