Answered

Welcome to Westonci.ca, the place where your questions are answered by a community of knowledgeable contributors. Get immediate and reliable solutions to your questions from a community of experienced experts on our Q&A platform. Get quick and reliable solutions to your questions from a community of experienced experts on our platform.

On the package for a certain brand of spinach seeds there is a guarantee that, if the printed instructions are followed, of planted seeds will germinate. A random sample of seeds is chosen. If these seeds are planted according to the instructions, find the probability that of them germinate.

Sagot :

The question is incomplete. Here is the complete question.

On the package for a certain brand of spinach seeds there is a guarantee that, if the printed instructions are followed, 63% of planted seeds will germinate. A random sample of 9 seeds is chosen. If these seeds are planted according to the instructions, find the probability that 4 or 5 of them germinate. Do not round your intermiediate computations, and round your answer to three decimal places.

Answer: P(4<X<5) = 0.624

Step-by-step explanation: The probability of a seed germinate is a Binomial Distribution, i.e., a discrete probability distribution of the number of successes in a sequence of n independents experiments.

This distribution can be approximated to normal distribution by determining the values of mean and standard deviation population:

[tex]\mu=np[/tex]

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

where

n is the sample quantity

p is proportion of successes

For the spinach seeds:

Mean is

[tex]\mu=9(0.65)[/tex]

[tex]\mu=[/tex] 5.85

Standard deviation is

[tex]\sigma=\sqrt{9.0.65(1-0.65)}[/tex]

[tex]\sigma=[/tex] 1.431

Now, use

[tex]z=\frac{x-\mu}{\sigma}[/tex]

to convert into a standard normal distribution.

The probability we want is between 2 values: P(4<X<5).

Therefore, we have to convert those two values:

For X = 4:

[tex]z=\frac{4-5.85}{1.431}[/tex]

z = -1.29

For X = 5:

[tex]z=\frac{5-5.85}{1.431}[/tex]

z = -0.59

Using z-table:

P(X>4) = 1 - P(z< -1.29) = 0.9015

P(X<5) = P(z< -0.59) = 0.2776

The probability will be

P(4<X<5) = P(X>4) - P(X<5)

P(4<X<5) = 0.9015 - 0.2776

P(4<X<5) = 0.624

The probability of 4 or 5 seeds germinate is 0.624.

Thanks for stopping by. We strive to provide the best answers for all your questions. See you again soon. Thanks for using our service. We're always here to provide accurate and up-to-date answers to all your queries. We're glad you visited Westonci.ca. Return anytime for updated answers from our knowledgeable team.