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Kisachek [45]
3 years ago
7

A class has 20 students. If the teacher is randomly selecting a group of 3 students to represent the class on the student counci

l, what is the probability that Sarah and her two best friends will all be chosen?
1/20
3/20
1/1,140
Mathematics
2 answers:
svet-max [94.6K]3 years ago
7 0
Answer is C. 1/1,140
Stolb23 [73]3 years ago
7 0

Answer:

P(Sarah and her two best friends will all be chosen)=1/1140

Step-by-step explanation:

A class has 20 students.

The teacher is randomly selecting a group of 3 students to represent the class on the student council.

The number of ways of choosing 3 students out of 20= 20_{C_{3}}

                                                                                          = 1140

we have to find the probability that Sarah and her two best friends will all be chosen.

That means Sarah and her friends are one group to be chosen.

Hence, P(Sarah and her two best friends will all be chosen)=1/1140

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Answer:

P(\bar X

And we can solve this using the following z score formula:

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And if we use this formula we got:

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P( Z

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".  

Solution to the problem

Let X the random variable that represent the heights of a population, and for this case we know the distribution for X is given by:

X \sim N(63.6,2.5)  

Where \mu=63.6 and \sigma=2.5

We select n =100. Since the distribution for X is normal then we know that the distribution for the sample mean \bar X is given by:

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We want this probability:

P(\bar X

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z = \frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n}}}

And if we use this formula we got:

z = \frac{63-63.6}{\frac{2.5}{\sqrt{100}}}= -2.4

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P( Z

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