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Chapter 6: Q. 78 (page 404)

78. Rhubarb Refer to Exercise 76. Would you be surprised if 3 or more of the plants in the bundle die before producing any rhubarb? Calculate an appropriate probability to support your answer.

Short Answer

Expert verified

The probability is less than 5%,ThereforeP(X≥3)=1.16%and the result is surprising.

Step by step solution

01

Given information

Three or more of the plants in the bundle die before producing any rhubarb.

02

Explanation

Given, n=10and p=0.05

The Binomial Probability:

P(X=k)=nk×pk×(1−p)n−k

P(X=0)=100×(0.05)0×(0.95)10−0≈0.5987

P(X=1)=101×(0.05)1×(0.95)10−1≈0.315

P(X=2)=102×(0.05)2×(0.95)10−2≈0.0746

P(X≥3)=1−P(X=0)−P(X=1)−P(X=2)=1−0.5987−0.3151−0.0746=0.0116=1.16%

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