Question

Exercise 1: 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 0:75. Let X be the number of plants with red petals resulting from 100 seeds from this cross that were collected and germinated.

a. Is it appropriate to approximate the distribution using the normal distribution? Explain Steps.

b. Use an appropriate method to find the approximate probability that between 70 and 80 (inclusive) offspring plants have red flowers. Here give the appropriate formula for the probability.

c. Calculate the approximate probability that 53 or fewer offspring plants had red flowers? Is this an unusual occurrence?

Answer 1

Given,

Probability of success, p = 0.75

Sample size, n = 100

np = 75, n(1 - p) = 25

(a) Since both np and n(1 - p) are greater than 10, it is appropriate to approximate the distribution using the normal distribution

Mean = np = 75

Standard deviation = = 4.33

(b) The required probability = P(70 ≤ X ≤ 80)

Using correction of continuity, the required probability

= P(69.5 < X < 80.5)

= P{(69.5 - 75)/4.33 < Z < (80.5 - 75)/4.33}

= P(-1.155 < Z < 1.155)

= 0.7518

(c) The probability that 53 or fewer offspring plants had red flowers = P(X ≤ 53)

Using correction of continuity, the required probability

= P(X < 53.5)

= P{Z < (53.5 - 75)/4.33}

= P(Z < -4.965)

≈ 0

Yes, this is an unusual occurrence