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BlackZzzverrR [31]
2 years ago
14

In a certain Algebra 2 class of 26 students, 5 of them play basketball and 12 of them play baseball. There are 12 students who p

lay neither sport. What is the probability that a student chosen randomly from the class plays basketball or baseball?
Mathematics
1 answer:
loris [4]2 years ago
6 0

Answer:\dfrac{7}{13}

Step-by-step explanation:

There are only two games basketball and baseball.

Any student who plays could play basketball or baseball.

Given that there are 26 students in total.

Given that there are 12 students who don't play any game at all.

So,there are 26-12=14 students who play play some baseball or basketball.

Probability=\frac{\text{number of favourable outcomes}}{\text{total number of outcomes}}

The required probability is \frac{14}{26}=\frac{7}{13}

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An amount of $19,000 is borrowed for 6 years at 7.25% interest, compounded annually. If the loan is paid in full at the end of t
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2 years ago
It seems to you that fewer than half of people who are registered voters in the City of Madison do in fact vote when there is an
Ad libitum [116K]

Answer:

a) Going to public places like restaurants, parks, theaters, etc in Madison and asking voters.

b) The 80% CI to estimate the true proportion of registered voters in the City of Madison who vote in non-presidential elections is (0.5533, 0.6667).

c) We are 80% sure that our confidence interval contains the true proportion of registered voters in the City of Madison who vote in non-presidential elections.

d) The lower limit of the interval is higher than 0.5. This means that it does seem that MORE than half of registered voters in the City of Madison vote in non-presidential elections.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of \pi, and a confidence interval 1-\alpha, we have the following confidence interval of proportions.

\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}

In which

Z is the zscore that has a pvalue of 1 - \frac{\alpha}{2}.

(a) How might a simple random sample have been gathered?

Going to public places like restaurants, parks, theaters, etc in Madison and asking voters.

(b) Construct an 80% CI to estimate the true proportion of registered voters in the City of Madison who vote in non-presidential elections.

You take an SRS of 200 registered voters in the City of Madison, and discover that 122 of them voted in the last non-presidential election. This means that n = 200, \pi = \frac{122}{200} = 0.61.

We want to build an 80% CI, so \alpha = 0.20, z is the value of Z that has a pvalue of 1 - \frac{0.20}{2} = 0.90[tex], so [tex]z = 1.645.

The lower limit of this interval is:

\pi - z\sqrt{\frac{\pi(1-\pi)}{200}} = 0.61 - 1.645\sqrt{\frac{0.61*0.39}{200}} = 0.5533

The upper limit of this interval is:

\pi + z\sqrt{\frac{\pi(1-\pi)}{200}} = 0.61 + 1.645\sqrt{\frac{0.61*0.39}{200}} = 0.6667

The 80% CI to estimate the true proportion of registered voters in the City of Madison who vote in non-presidential elections is (0.5533, 0.6667).

(c) Interpret the interval you created in part (b).

We are 80% sure that our confidence interval contains the true proportion of registered voters in the City of Madison who vote in non-presidential elections.

(d) Based on your CI, does it seem that fewer than half of registered voters in the City of Madison vote in non-presidential elections? Explain.

The lower limit of the interval is higher than 0.5. This means that it does seem that MORE than half of registered voters in the City of Madison vote in non-presidential elections.

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