|STAT 13 (1a,
1b, 1c, 1d)
Methods for the Life and Health Science
|Department of Statistics
Instructor: Ivo Dinov
|Due Date: Wednesday, May 08, 2013
- (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 <=47).
- P(32 <= ED <=43).
- P(46 <= ED).
- P(57 <= ED).
- P(41 <= ED <=81).
- P(22 <= ED <=53).
- (HW.4.2) Suppose
that the serum
cholesterol levels of 17-year-olds follows a normal distribution with
mean 178 mg/dLi and standard deviation 31 mg/dLi. What percentage of
17-year-olds have serum cholesterol values:
- 172 or less?
- 170 or more?
- 215 or less?
- 132 or more?
- between 171 and 201?
- between 125 and 153?
- between 156 and 189?
- (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 6.3 and standard deviation 1.8. Let Y be the
size of a randomly chosen litter. Use the Normal
Distribution calculator to find approximate
- P(Y <= 6)
- P(Y = 8)
- P(5 <= Y <= 10)
- (HW.4.5) A survey
DNA variation in smelts
in a lake
revealed that 2 haplotypes
(genotypes) were present in the population.
33% of the fish were of haplotype A, and the remaining 67% were
haplotype B. If we sample 400 fish from the lake, what is the
- at least 140 are haplotype A?
- at least 260 are haplotype B?
- Between 120 and 150 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. Suppose the change in heart rate follows a normal
distribution, with mean increase of
6.5 beats per minute and a standard
deviation of 9.1. Let Y denote the
change in heart rate for a randomly
selected person. Find:
- P(Y > 8).
- P(Y > 17).
- P(7 < Y < 16).