Ivo Dinov
UCLA Statistics, Neurology, LONI
, Math/PIC
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STAT 13 (1a, 1b, 1c)

Introduction to Statistical Methods for the Life and Health Science

Department of Statistics

## Instructor: Ivo Dinov

Homework 4
Due Date: Wednesday, Nov. 05, 2008

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 = 1,400g and standard deviation 100g. Let Y denote the brain weight of a randomly chosen person from this population. Calculate:
• P(Y <=1,500).
• P(1,325 <= Y <=1,500).
• P(1,325 <= Y).
• P(1,475 <= Y).
• P(1,475 <= Y <=1,600).
• P(1,200 <=Y <=1,325).

• 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:
• 186 or more?
• 156 or less?
• 216 or less?
• 121 or more?
• between 186 and 216?
• between 121 and 156?
• between 156 and 186?

• The June precipitation totals, in inches" for the city of Cleveland, OH are given below. Use these values to create a normal probability plot of the data. Do you conclude that these data are Normally distributed?

 Year Rainfall Normal_Score 1964 2.06 -0.94 1965 3.05 -0.52 1966 1.83 -1.23 1967 1.17 -1.71 1968 2.32 -0.71 1969 4.61 0.52 1970 4.98 0.94 1971 3.79 0.16 1972 9.06 1.71 1973 6.72 1.23 1974 3.57 -0.16 1975 4.10 0.33 1976 3.64 0.00 1977 4.91 0.71 1978 3.30 -0.33
• The litter size of a certain population of female mice follows approximately a normal distribution with mean 7.8 and standard deviation 2.3. Let Y be the size of a randomly chosen litter. Use Normal approximation to Binomial Distribution to find approximate values for these probabilities. Then compare these to the corresponding exact Binomial probabilities.
• P(Y <= 6)
• P(Y = 6)
• P8 <= 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 125 are haplotype A?
• 180 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; the subjects then 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 7.3 beats per minute and a standard deviation of 11.1. Let Y denote the change in heart rate for a randomly selected person. Find:
• P(Y > 10).
• P(Y > 20).
• P(5 < Y < 15).

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