Homework Sourse1331 According to genetic theory the blossom color in the se
(13.31) According to genetic theory, the blossom color in the second generation of a certain cross of sweet peas should be red or white in a 3:1 ratio.
That is, each plant has probability 3/4 of having red blossoms, and the blossom colors of separate plants are independent.
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| 1. | What is the probability that exactly 2 out of 8 of these plants have red blossoms? | ||||||||
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Solution
(13.31) According to genetic theory, the blossom color in the second generation of a certain cross of sweet peas should be red or white in a 3:1 ratio.
That is, each plant has probability 3/4 of having red blossoms, and the blossom colors of separate plants are independent.
1.
What is the probability that exactly 2 out of 8 of these plants have red blossoms?
A.
0.0038
B.
0.1780
C.
0.3115
D.
0.2651
P=3/4=0.75
n=8
P(X=x) = (nCx) px (1-p)n-x
P(X=2) = (8C2) 0.752 (1-0.75)8-2
P(X = 2) = 0.0038
2.
What is the mean number of red-blossomed plants when 72 plants of this type are grown from seeds?
Expectation mean = np = 72*0.75= 54
A.
54
B.
72
C.
18
D.
36
3.
What is the probability of obtaining at least 50 red-blossomed plants when 80 plants are grown from seeds? Use the Normal approximation if applicable.
A.
0.0125
B.
0.9875
C.
0.9951
D.
0.0049
E.
0.1250
F.
0.8750
n=80
Expectation = np = 60
Variance = np(1 - p) = 15
Standard deviation =sqrt( variance) = 3.873
Z value for 50, z=(50-60) /3.873 =2.58
P( x >=50) = p( z >2.58) =0.0049 ( from standard normal table)
| 1. | What is the probability that exactly 2 out of 8 of these plants have red blossoms? | ||||||||||
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