4: Probability Distributions
Students apply the normal distribution to calculate probabilities, use z-tables, and identify properties of probability distributions.
Hardy-Weinberg Variables from Population Data
Click to show Hardy-Weinberg Variables from Population Data example problem
In the desert population of 625 snakes, there were 441 with diamond pattern scale pattern, 168 with striped pattern scale pattern, and 16 with solid color scale pattern.
The researcher calculates a fraction of
| 1 × 168 + 2 × 16 |
| 1,250 |
Which Hardy-Weinberg variable below is represented by the value 0.16?
Hardy-Weinberg Allele and Genotype Frequencies from Population Data (Numeric)
Click to show Hardy-Weinberg Allele and Genotype Frequencies from Population Data (Numeric) example problem
| snakes | ||
|---|---|---|
| genotype | phenotype | count |
| homozygous dominant | red | 5,019 |
| heterozygous | pink | 10,962 |
| homozygous recessive | white | 9,019 |
| SUM | 25,000 | |
In a field there are 5,019 red snakes, 10,962 pink snakes, and 9,019 white snakes that show incomplete dominance. What is the frequency of the dominant allele?
Note: Do not enter a percentage on the blank. For example, if the answer is 32.5%, enter 0.325 on the blank. Your answer will be a decimal value between 0 and 1.
Parent Genotypes in X-Linked Recessive Crosses
Click to show Parent Genotypes in X-Linked Recessive Crosses example problem
The white-eyed (mutant) phenotype is an X-linked recessive disorder in fruit flies. The red-eyed (wildtype) allele, +, is dominant to the white (mutant) allele, w. The offspring of size 480 from the mating of a single female (♀) and a single male (♂) are shown in the table below:
| phenotype | female (♀) | male (♂) |
|---|---|---|
| red-eyed (wildtype) | 238 | 0 |
| white-eyed (mutant) | 0 | 242 |
What are the genotypes of the parents in this cross?
Offspring Sex Distribution Using the Binomial Model
Click to show Offspring Sex Distribution Using the Binomial Model example problem
Model: Binomial →
| ⟮ | n | ⟯ |
| k |
In this scenario, assume that each child is born independently with the same chance of being either sex. The event outcomes are mutually exclusive, so we can apply the binomial model to determine the probability of a specific combination.
A woman has eight (8) children. What is the probability that she has exactly six (6) boys ♂ and two (2) girls ♀?