Plant Genetics In Exercise 5.75, a cross between two peony plants—one with red petals and one with streaky petals—produced offspring plants with red petals 75% of the time. Suppose that 100 seeds from this cross were collected and germinated, and x, the number of plants with red petals, was recorded.
a. What is the exact probability distribution for x?
b. Is it appropriate to approximate the distribution in part a using the normal distribution? Explain.
c. Use an appropriate method to find the approximate probability that between 70 and 80 (inclusive) offspring plants have red flowers.
d. What is the probability that 53 or fewer offspring plants had red flowers? Is this an unusual occurrence?
e. If you actually observed 53 of 100 offspring plants with red flowers, and if you were certain that the genetic ratio 3:1 was correct, what other explanation could you give for this unusual occurrence?
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Plant Genetics A peony plant with red petals was crossed with another plant having streaky petals. The probability that an offspring from this cross has red flowers is .75. Let x be the number of plants with red petals resulting from ten seeds from this cross that were collected and germinated.
a. Does the random variable x have a binomial distribution? If not, why not? If so, what are the values of n and p?
b. Find P(x ≥ 9).
c. Find P(x≤ 1).
d. Would it be unusual to observe one plant with red petals and the remaining nine plants with streaky petals? If these experimental results actually occurred, what conclusions could you draw?
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