{ In a recent basketball game, a player who makes 65% of his free throws made eight consecutive free throws. Assuming that free-throw shots are independent, determine whether this feat was unusual. }
I'm just a little lost on how to determine if it's unusual or not.
I have this so far:
.65 x .65 x .65 x .65 x .65 x .65 x .65 x .65 = .0318644813
So generally, doing this would be a 3.2% chance. Does that mean that it's unusual he did this?
Yes, if you are using P = .05 as level of significance. However, no, if you are using P = .01.
Well, that's a great math calculation you've done there! But let me add a little clown humor to help you determine whether this feat was unusual.
Let's imagine a scenario where you invite your friends over for a game of basketball. You confidently tell them, "Hey, watch me make eight consecutive free throws!" As the game starts, you step up to the free-throw line with a goofy grin on your face.
You shoot the first one and it goes in. Your friends cheer, thinking, "Hey, maybe he's got a lucky streak going!"
You shoot the second one, and it also goes in. Now they're starting to get skeptical, but they're still cheering you on.
You shoot the third one, and it goes in again. Now your friends are looking at each other, thinking, "Is this really happening?"
You continue making more shots, and with each one that goes in, your friends' jaws drop a little lower. By the time you've made eight in a row, they're completely amazed and in awe of your basketball skills.
So, was it unusual that you made eight consecutive free throws? Absolutely! It's not something that you see every day, and your friends would probably be talking about it for weeks.
In conclusion, based on the math and the clown-approved humor, it is indeed unusual for a player who makes 65% of his free throws to make eight consecutive shots. Well done, basketball magician!
To determine whether the player's feat was unusual, you can calculate the probability of making eight consecutive free throws assuming independence.
The probability of making any single free throw is 65% or 0.65. To calculate the probability of making eight consecutive free throws, you need to multiply the probability of making a free throw by itself eight times because each free throw is independent of the others.
So, the calculation would be:
0.65 x 0.65 x 0.65 x 0.65 x 0.65 x 0.65 x 0.65 x 0.65 = 0.0318644813
This means the probability of making eight consecutive free throws is approximately 0.0319 or 3.19%.
Now, whether this is considered unusual or not depends on the context and what you consider to be the threshold for unusual. If you consider a 3.19% probability low enough to be unusual, then yes, the player's feat would be considered unusual.
To determine whether the player's feat of making eight consecutive free throws is unusual or not, you are on the right track by calculating the probability.
First, let's clarify the calculation you've done. Since the player makes 65% of his free throws, the probability of making one free throw is 0.65 (or 65%). Assuming independence, the probability of making eight consecutive free throws can be calculated by multiplying the individual probabilities together.
So your calculation should be:
0.65 x 0.65 x 0.65 x 0.65 x 0.65 x 0.65 x 0.65 x 0.65 ≈ 0.1071
The result you computed, 0.0318644813, seems to be the probability for seven consecutive free throws, not eight.
Now, to determine whether the feat is unusual, we need to establish a threshold for what is considered unusual. This threshold is a matter of interpretation and can vary depending on the context. A common practice is to consider probabilities below 0.05 (or 5%) as unusual.
In this case, the probability of making eight consecutive free throws is approximately 0.1071, which is higher than the threshold of 0.05. Thus, based on this calculation alone, it would not be considered unusual for the player to make eight consecutive free throws.
However, it is important to note that this analysis assumes independence between each free throw attempt. In reality, a player's performance can fluctuate, and factors such as fatigue, pressure, and skill level can come into play.
So, while the calculation suggests it is not unusual, it is always important to consider other factors and context when evaluating the uniqueness of a specific performance.