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A very common dahlia plant with red petals is crossed with another very common 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 flowers grown from 100 randomly collected seeds from a very large population (N > 10,000) of this cross. A. Does the random variable X have a binomial distribution

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Answer:

Yes, it is vivid that the random variable has a binomial distribution

Explanation:

From the given information:

The probability of the plant with red flowers(p success) = 0.75

the sample size n = 100

Thus, the mean μ = np

= 100 ×0.75

= 75

The standard deviation can be calculated by using the formula:

[tex]SD = \sqrt{np(1-p)}[/tex]

[tex]SD = \sqrt{100 \times 0.75(1-0.75)}[/tex]

[tex]SD = \sqrt{100 \times 0.75(0.25)}[/tex]

[tex]SD = \sqrt{18.75}[/tex]

SD = 4.33

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