Ivo Dinov
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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, May 08, 2013

Please, submit your homework before lecture on the due date. See the HW submission rules. On the front page include the following header.
Complete the following problems using the interactive SOCR Normal Distribution calculator. Include snapshots of all of your work to support your findings.
• (HW.4.1) There is a great 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 page). 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 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?

• (HW.4.4) The litter size 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 values for these probabilities:
• P(Y <= 6)
• P(Y = 8)
• P(5 <= Y <= 10)

• (HW.4.5) A survey of mitochondrial 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 probability that:
• 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).

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