Chapter 6: Q. 79 (page 404)

79. Sowing seeds Refer to Exercise 69.
(a) Find the probability that exactly $17$ seeds germinate. Show your work.
(b) If only $12$ seeds actually germinate, should Judy be suspicious that the company’s claim is not true? Compute $P (X \leq 12)$ and use this result to support your answer.

Short Answer

Expert verified

(a) The probability that exactly $17$ seeds germinate is $P (X = 17) = 24.28 %$ .

(b) Judy should be suspicious and the value is $P (X \leq 12) \approx 0.0059 \approx 0.59 %$ .

Step by step solution

Part (a) Step 1: Given information

The probability for the exactly $17$ seeds germinate.

Part (a) Step 2: Explanation

Given: $n = 20$ , and $p = 0.85$
The Binomial Probability:
$P (X = k) = (\begin{matrix} n \\ k \end{matrix}) \times p^{k} \times (1 - p)^{n - k}$

$P (X = 17) = (\begin{matrix} 20 \\ 17 \end{matrix}) \times (0.85)^{17} \times (0.15)^{20 - 17} \approx 0.2428 = 24.28 %$

Part (b) Step 1: Given information

Let, $12$ seeds actually germinate. And compute the value $P (X \leq 12)$ .

Part (b) Step 2: Explanation

Given: $n = 20$ , and $p = 0.85$ .

Let's use the binomial Probability:

$P (X = k) = (\begin{array}{l} n \\ k \end{array}) \times p^{k} \times (1 - p)^{n - k}$
$P (X \leq 12) = P (X = 0) + P (X = 1) + \dots + P (X = 12) \approx 0.0059 \approx 0.59 %$

As a result, the probability is low (less than $0.05$ ), indicating that the event is unlikely to happen by chance.

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79. Sowing seeds Refer to Exercise 69.
(a) Find the probability that exactly $17$ seeds germinate. Show your work.
(b) If only $12$ seeds actually germinate, should Judy be suspicious that the company’s claim is not true? Compute $P (X \leq 12)$ and use this result to support your answer.

Short Answer

Step by step solution

Part (a) Step 1: Given information

Part (a) Step 2: Explanation

Part (b) Step 1: Given information

Part (b) Step 2: Explanation

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79. Sowing seeds Refer to Exercise 69.(a) Find the probability that exactly17 seeds germinate. Show your work.(b) If only 12seeds actually germinate, should Judy be suspicious that the company’s claim is not true? Compute P(X≤12)and use this result to support your answer.

Short Answer

Step by step solution

Part (a) Step 1: Given information

Part (a) Step 2: Explanation

Part (b) Step 1: Given information

Part (b) Step 2: Explanation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Probability and Statistics

Theoretical and Mathematical Physics

Calculus

Discrete Mathematics

Geometry

Study anywhere. Anytime. Across all devices.

79. Sowing seeds Refer to Exercise 69.
(a) Find the probability that exactly $17$ seeds germinate. Show your work.
(b) If only $12$ seeds actually germinate, should Judy be suspicious that the company’s claim is not true? Compute $P (X \leq 12)$ and use this result to support your answer.