Question

A well-mixed cookie dough will produce cookies with a mean of 6 chocolate chips apiece. What is the probability of getting a cookie with no more than 3 chips? Round your answer to four decimal places.

Answer 1

The probability of getting a cookie with no more than 3 chips is 0.714.

What is probability?

It is defined as the ratio of the number of favorable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.

We have:

Well-mixed cookie dough will produce cookies with a mean of 6 chocolate chips apiece.

Using poison ratio:

$\rm P (X = k) = \dfrac{\lambda^k e^{-\lambda}}{k!}$

λ is the mean number of chocolate chips in a piece

$\rm P (X = 6) = \dfrac{6^k e^{-6}}{k!}$

P(X ≥ 5) = 1 - P(X < 5)

P(X ≥ 5) = 1 - P(X = 0) + P(X = 1)  + P(X = 2)  + P(X = 3) + P(X = 4)  

$\rm P(X \geq 5) = 1-[\dfrac{6^0 e^{-6}}{0!}+\dfrac{6^1 e^{-6}}{1!}+\dfrac{6^2 e^{-6}}{2!}+\dfrac{6^3 e^{-6}}{3!}+\dfrac{6^4 e^{-6}}{4!}]$

After solving;

P(X ≥ 5) = 0.714

Thus, the probability of getting a cookie with no more than 3 chips is 0.714.

Learn more about the probability here:

brainly.com/question/11234923

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