|STAT 13 (1a,
Methods for the Life and Health Science
|Department of Statistics
Instructor: Ivo Dinov
|Due Date: Wednesday, Nov. 05, 2008
- (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?
- 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
- P(Y <= 6)
- P(Y = 6)
- P8 <= Y <= 11)
- A survey of
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 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.
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).