How many more vertices does a rectangular prism have, compared to triangular pyramid?

David's chance of making a free throw is 80%. In a game, he takes 10 free throws. What is the probability he makes 8 or fewer fr

maks197457 [2]

Answer:

$P(X\leq 8)= 1- P(X>8) = 1-P(X\geq 9)= 1-[P(X=9)+P(X=10)]$

And we can find the individual probabilities like this:

$P(X=9)=(10C9)(0.8)^{9} (1-0.8)^{10-9}$

$P(X=10)=(10C10)(0.8)^{10} (1-0.8)^{10-10}$

And replacing we got:

$P(X\leq 8)=1-[10(0.8)^1 (1-0.8)^{1} + (0.8)^{10}]$

Step-by-step explanation:

Previous concepts

A Bernoulli trial is "a random experiment with exactly two possible outcomes, "success" and "failure", in which the probability of success is the same every time the experiment is conducted". And this experiment is a particular case of the binomial experiment.

The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".

The probability mass function for the Binomial distribution is given as:

$P(X)=(nCx)(p)^x (1-p)^{n-x}$

Where (nCx) means combinatory and it's given by this formula:

$nCx=\frac{n!}{(n-x)! x!}$

The complement rule is a theorem that provides a connection between the probability of an event and the probability of the complement of the event. Lat A the event of interest and A' the complement. The rule is defined by: $P(A)+P(A') =1$

Solution to the problem

For this case we want this probability:

$P(X\leq 8)$

And for this case we can use the comlement rule and we got:

$P(X\leq 8)= 1- P(X>8) = 1-P(X\geq 9)= 1-[P(X=9)+P(X=10)]$

And we can find the individual probabilities like this:

$P(X=9)=(10C9)(0.8)^9 (1-0.8)^{10-9}$

$P(X=10)=(10C10)(0.8)^{10} (1-0.8)^{10-10}$

And replacing we got:

$P(X\leq 8)=1-[10(0.8)^9 (1-0.8)^{1} + (0.8)^{10}]$

4 0

3 years ago

draw 8 lines that are between 1 inch and 4 inches long. measure each line to the nearest four inch, and make a line plot.

dybincka [34]

Attached you can find the answer to your question.

What you have to do is:
1. Draw 8 lines between 1 inch and 4 inches.
2. Create a line plot (count how many times each length occurs)
3. Congratulations! That's it!

Hope it is clear!

5 0

3 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.

4 0

3 years ago

Which choice includes all of the solutions to 2x2 + x – 3 = 0 by factoring

KonstantinChe [14]

Answer:either c or b

Step-by-step explanation: to be honest I searched up

3 0

3 years ago

Read 2 more answers

In an automobile parts factory, for every 175 carburetors 3 are found to be defective. At that rate how many carbureatots out of

Furkat [3]

Answer: