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raketka [301]
2 years ago
12

Based on a study from the Chronicles of Flippin'' Awesomeness, the probability that Napoleon and Pedro make it to their first pe

riod class on time is 0.26. The probability that Napoleon and Pedro catch the bus is 0.25. However, the probability that they make it to their first period class on time, given that they catch the bus is 0.61. What is the probability that Napoleon and Pedro catch the bus and make it to their first period class on time
Mathematics
1 answer:
muminat2 years ago
8 0

Answer:

15.25% probability that Napoleon and Pedro catch the bus and make it to their first period class on time

Step-by-step explanation:

We use the conditional probability formula to solve this question. It is

P(B|A) = \frac{P(A \cap B)}{P(A)}

In which

P(B|A) is the probability of event B happening, given that A happened.

P(A \cap B) is the probability of both A and B happening.

P(A) is the probability of A happening.

In this problem, we have that:

Event A: Both Napoleon and Pedro catch the bus, so P(A) = 0.25.

Event B: Making to their first period class on time.

However, the probability that they make it to their first period class on time, given that they catch the bus is 0.61.

This means that P(B|A) = 0.61

What is the probability that Napoleon and Pedro catch the bus and make it to their first period class on time

P(B|A) = \frac{P(A \cap B)}{P(A)}

0.61 = \frac{P(A \cap B)}{0.25}

P(A \cap B) = 0.61*0.25

P(A \cap B) = 0.1525

15.25% probability that Napoleon and Pedro catch the bus and make it to their first period class on time

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Step-by-step explanation:

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(1/2) ÷ (1/4) = (1/2) × (4/1) = 2

That doesn’t help you answer this particular question, though.

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A brewery produces cans of beer that are supposed to contain exactly 12 ounces. But owing to the inevitable variation in the fil
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Answer:

T \sim N (\mu = 6*12=72 , \sigma= \sqrt{6} *0.3=0.735)

P(T \leq 72) = P(Z< \frac{72-72}{0.735}) = 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".  

Solutio to the problem

Let X the random variable that represent the amount of beer in each can of a population, and for this case we know the distribution for X is given by:

X \sim N(12,0.3)  

Where \mu=12 and \sigma=0.3

For this case we select 6 cans and we are interested in the probability that the total would be less or equal than 72 ounces. So we need to find a distribution for the total.

The definition of sample mean is given by:

\bar X = \frac{\sum_{i=1}^n X_i}{n} = \frac{T}{n}

If we solve for the total T we got:

T= n \bar X

For this case then the expected value and variance are given by:

E(T) = n E(\bar X) =n \mu

Var(T) = n^2 Var(\bar X)= n^2 \frac{\sigma^2}{n}= n \sigma^2

And the deviation is just:

Sd(T) = \sqrt{n} \sigma

So then the distribution for the total would be also normal and given by:

T \sim N (\mu = 6*12=72 , \sigma= \sqrt{6} *0.3=0.735)

And we want this probability:

P(T\leq 72)

And we can use the z score formula given by:

z = \frac{x-\mu}{\sigma}

P(T \leq 72) = P(Z< \frac{72-72}{0.735}) = P(Z

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