The alleles for black (B) and white (b) feather color in chickens show incomplet
ID: 3150374 • Letter: T
Question
The alleles for black (B) and white (b) feather color in chickens show incomplete dominance; individuals with the gene pair Bb have "blue" feathers. When one individual that is homozygous dominant (BB) for this trait is mated with an individual that is homozygous recessive (bb) for this trait, 1/2 will carry the gene pair Bb. Let x be the number of chicks with "blue" feathers in a sample of n = 15 chicks resulting from this type of cross.
A) What is the mean number of chicks with "blue" feathers in the sample?
B) What is the probability of observing fewer than six chicks with "blue" feathers? (Round your answer to three decimal places.)
C) What is the probability that the number of chicks with "blue" feathers is greater than or equal to 9 but less than or equal to 11? (Round your answer to three decimal places.)
Explanation / Answer
a)
As
n = 15, p = 1/2 = 0.5, then
u = mean = n p = 15*0.5 = 7.5 [ANSWER]
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b)
Note that P(fewer than x) = P(at most x - 1).
Using a cumulative binomial distribution table or technology, matching
n = number of trials = 15
p = the probability of a success = 0.5
x = our critical value of successes = 6
Then the cumulative probability of P(at most x - 1) from a table/technology is
P(at most 5 ) = 0.150878906
Which is also
P(fewer than 6 ) = 0.150878906 [ANSWER]
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c)
Note that P(between x1 and x2) = P(at most x2) - P(at most x1 - 1)
Here,
x1 = 9
x2 = 11
Using a cumulative binomial distribution table or technology, matching
n = number of trials = 15
p = the probability of a success = 0.5
Then
P(at most 8 ) = 0.696380615
P(at most 11 ) = 0.982421875
Thus,
P(between x1 and x2) = 0.28604126 [ANSWER]
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