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UCLA Statistics, Neurology, LONI, Math/PIC

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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: Monday, Feb. 08, 2010

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 = 1,350g and standard deviation 95g. Let Y denote the brain weight of a randomly chosen person from this population. Calculate:

P(Y <=1,400).
P(1,325 <= Y <=1,400).
P(1,325 <= Y).
P(1,450 <= Y).
P(1,450 <= 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 more?
166 or less?
212 or less?
123 or more?
between 176 and 206?
between 123 and 157?
between 155 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 consider these data to be 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 8.0 and standard deviation 2.1. Let Y be the size of a randomly chosen litter. Use the Normal Distribution 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 120 are haplotype A?
at least 310 are haplotype B?
Between 125 and 145 are haplotype A?
170 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 7.1 beats per minute and a standard deviation of 10.9. Let Y denote the change in heart rate for a randomly selected person. Find:

P(Y > 9).
P(Y > 19).
P(6 < Y < 14).

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