# 2014 Problem Set 2

**Topics:**Normal distribution, Binomial distribution, Poisson distribution

**Pages:**2 (605 words)

**Published:**June 21, 2015

1.

A population of marine gastropods has shell lengths that are normally distributed with a mean μ = 8 mm and variance σ2 = 2.15 mm2.

a. what proportion of the population will have shell lengths between 6.5 mm and 8.5 mm? (3 points)

b. what is the probability of finding a gastropod that has a shell length of exactly 7.5 mm? (1 point)

c. if there are 1,000 gastropods in an area, how many will have shell lengths greater than 5 mm? (3 points)

2.

Childhood lead poisoning is a public health concern in most urban areas. In a certain population, 1 child in 10 has a high blood-lead level (defined as 30 μg/dl or more). In a randomly chosen group of 16 children from this population, what is the probability that a. none has high blood lead (2 points)

b. 3 or fewer have high blood lead (2 points)

c. more than 4 have high blood lead (2 points)

d. What is the expected number that will have high blood lead? (2 points) 3.

In a study of the effectiveness of an insecticide against gypsy moths, Lymantria dispar, a large area of land was sprayed. Later, the area was examined for live adult insects by randomly selecting and surveying 10m x 10m squares. Past experience has shown the average number of live adult insects per square after spraying to be 5. If these insects are Poissonally distributed, find

a. the probability that a square will contain exactly 4 live adult insects (2 points) b. f(3) ( 1 point)

c. the probability that a square will have more than 3 live adult insects. (2 points)

4.

Use the normal approximation to compute the probability that between 50 and 75 of 100 white blood cells will be neutrophils, where the probability that any one cell is a neutrophil is 0.6. These values are chosen as proposed limits to the range of neutrophils in normal people and we wish to predict what proportion of people will be in the normal range according to this definition. (5 points)

5.

The probability that a baby is born with a...

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