A total of 16 mice are sent down a maze, one by one. From previous experience, it is believed...

Question:

A total of 16 mice are sent down a maze, one by one. From previous experience, it is believed that the probability a mouse turns right is .38. Suppose their turning pattern follows a binomial distribution. Use the PDF or the CDF command to help answer each of the following questions.

a) What is the probability that exactly 8 of the 16 mice turn right?

b) What is the probability that 8 or fewer of the 16 mice turn right?

c) What is the probability that 8 or more turn right?

d) What is the probability that more than 3, but fewer than 10 turn right?

e) What is the probability that exactly 10 turn left?

Probability Under Binomial Distribution:

Binomial distribution is a Bernoulli experiment repeated over a given number of trials. The two possible outcomes are termed as success or failure. The number of successes are predetermined and fixed.

Answer and Explanation:

a).

Given that;

{eq}n=16\\p=0.38 {/eq}

{eq}P(x=8)=? {/eq}

Use formula or online calculator given by the link below to calculate the probability:

{eq}b(n,x,p)=^nC_xp^x(1-p)^{n-x} {/eq}

https://stattrek.com/online-calculator/binomial.aspx

{eq}P(X=8)=0.1222 {/eq}


b).

{eq}\begin{align*} P(x\le 8)&=P(x=0)+P(x=1)+P(x=2)+...P(x=8)\\&=0.8924 \end{align*} {/eq}


c).

{eq}\begin{align*} P(x\ge 8)&=P(x=8)+P(x=9)+...P(x=16)\\&=0.2298 \end{align*} {/eq}


d).

{eq}\begin{align*} P(3\le x\le 10)&=P(x\le 10)-P(x\le 3)\\&=0.9875-0.0881\\&=0.8994 \end{align*} {/eq}


e).

Subtract 0.38 from one to get the probability of mouse turning left:

{eq}P(x=0)=0.0005 {/eq}


Learn more about this topic:

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Binomial Theorem Practice Problems

from Math 101: College Algebra

Chapter 11 / Lesson 4
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