A local jam production company is confident that 60% of the population will like its new grapefruit jelly. From a random sample of 10 persons who tasted the new grapefruit jelly, calculate the probability that 3 will like it to 3

A local jam production company is confident that 60% of the population will like its new grapefruit jelly. From a random sample of 10 persons who tasted the new grapefruit jelly, calculate the probability that 3 will like it to 3

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Question

A local jam production company is confident that 60% of the population will like its new grapefruit jelly. From a
random sample of 10 persons who tasted the new grapefruit jelly, calculate the probability that 3 will Ilike it to 3
decimal places.
Answer:
Next page.
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Expert Solution

Step 1

From the given information, the probability of the population will like new grapefruit jelly is 60%.

There are10 persons.

The suitable distribution is binomial.

Let X follows Binomial distribution with parameters n=10 and p=0.60.

$P (X = x) = (\begin{matrix} n \\ x \end{matrix}) p^{x} {(1 - p)}^{n - x} = (\begin{matrix} 10 \\ x \end{matrix}) 0 . 60^{x} {(1 - 0.60)}^{10 - x}, x = 0, . . ., 10$

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