I have a test guys (One Smart Man Op Plays)

The probability that Shruti succeeds at any given free-throw is 80%, percent. She was curious how many free-throws she can expec

Nina [5.8K]

Answer:

The probability that she succeeds at 10 or more free-throws in a sample of 12 free-throws is 0.5584.

Step-by-step explanation:

For each free throw, there are only two possible outcomes. Either it is a success, or it is not. The probability of a free throw being a success is independent of other free throws. So we use the binomial probability distibution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

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

And p is the probability of X happening.

Sample of 12 free throws.

This means that $n = 12$

The probability that Shruti succeeds at any given free-throw is 80%, percent.

This means that $p = 0.8$

Probability that she succeeds at 10 or more free-throws in a sample of 12 free-throws.

$P(X \geq 10) = P(X = 10) + P(X = 11) + P(X = 12)$

Then

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 10) = C_{12,10}.(0.8)^{10}.(0.2)^{2} = 0.2835$

$P(X = 11) = C_{12,11}.(0.8)^{11}.(0.2)^{1} = 0.2062$

$P(X = 12) = C_{12,12}.(0.8)^{12}.(0.2)^{0} = 0.0687$

$P(X \geq 10) = P(X = 10) + P(X = 11) + P(X = 12) = 0.2835 + 0.2062 + 0.0687 = 0.5584$

The probability that she succeeds at 10 or more free-throws in a sample of 12 free-throws is 0.5584.

3 0

3 years ago

Read 2 more answers

An airplane flies with a constant speed of 620 miles per hour. How long will it take to

LekaFEV [45]

Answer:

30 minutes

Step-by-step explanation:

Alright lets start by laying out what the problem gives us :

A plane flies 620 mph.

It is asking how long it will take to travel 310 miles.

We need to give our answer in minutes or hours.

So lets take mph and look at the full meaning "Miles per hour"

An hour has 60 minutes in it.

So really it is saying miles per 60 minutes as well as miles per hour

So you could say the plane is traveling 620 miles every 60 minutes.

So now lets look at the number 310.

Just looking at it I can tell you that 310 looks very close to half of 620, in fact it is exactly half!

So lets divide the 620 mph by the 310 miles it is asking and we get 2! Proving that 310 is half of 620.

Alright now lets divide both the number of miles and number of minutes :

620 miles per 60 minutes

divided by 2 both miles and minutes

310 miles per 30 minutes

So this is your answer. After this you get that it would take 30 minutes to travel 310 miles in a plane going 620 miles per hour!

I hope this helps and I could help you understand it. :)

If you have any questions feel free to comment or dm me.

7 0

3 years ago

Squash and Water are mixed in the ratio 1:5. Marion needs to make cups of juice that are 150ml for a party. She anticipates she

PIT_PIT [208]

You need to add 1 and 5 and get 6
do 150 divided by 6
you get 25

6 0

3 years ago

A________ has cross-sectional shapes, taken parallel to a base, that are similar

alexdok [17]

Answer:

I think it is C

Step-by-step explanation

cube has equal sides and is parallel.

3 0

2 years ago

Please help me with this. Use the combination method of substitution to solve. Please show and explain work. Thanks.

Artemon [7]

Answer:

x = 25.35 (or 2129/84) and y = 4334.04 (or 121353/28)

Step-by-step explanation:

The given equations are set up and ready to go with substitution. Simply just plug in the first equation to the second equation as both are equal to y.

Step 1: Replace y in y = 87x + 2129 with 171x

171x = 87x + 2129

Step 2: Subtract 87 x on both sides

84x = 2129

Step 3: Divide both sides by 84 to get x

x = 2129/84 or 25.35 (rounded)

To get y, simply plug in x into one of the 2 original equations. In this case, I will use the first equation:

y = 171 (25.35)

y = 121353/28 or 4334.04 (rounded)

You can check your work by plugging both solutions into the calculator and see if they equal each other. The values for these answers are solely based on the equations, so if you write the equations wrong themselves, then that means you have the values wrong as well.

6 0

3 years ago