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oksian1 [2.3K]
3 years ago
14

Suppose a NBA basketball player has 5% chance of picking up a foul every minute he plays. What is the probability that he will p

lay the entire 48 minutes of the game without fouling out (i.e., without picking more than four fouls)?
Mathematics
1 answer:
alukav5142 [94]3 years ago
8 0

Answer:

He wont foul out with probability 0.9093

Step-by-step explanation:

The total number of fools he picked is a Binomial ditribution noted by X with parameters p = 0.05 and N = 48. The mean of this random variable is μ = np = 48*0.05 = 2.4 and the variance is σ² = np(1-p) = 2.4*0.95 = 2.28, hence its standard deviation is σ = √2.28 = 1.51.

Note that, if approximate probability is asked, we could just approximate X with a Normal random variable with mean 2.4 and standard deviation 1.51 (this can be done because of the central limit theorem). We will calculate the probability manually. He wont foul out if he picks 0,1,2,3 or 4 fouls, thus

P(X \leq 4) = P(X=0)+P(X=1)+P(X=2)+P(X=3)+P(X=4) \\= 0.95^{48}+48*0.95^{47}*0.05+{48 \choose 2}*0.95^{46}*0.05^2+\\{48 \choose 3}*0.95^{45}*0.05^3+{48 \choose 4}*0.95^{44}*0.05^4 \\= 0.085+0.215+0.266+0.215+0.127 = 0.9093

As a consecuence, he wont foul out with probability 0.9093.

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8
MakcuM [25]

Answer:  C) 4.20

Explanation:

Multiply each value with its corresponding frequency:

  • 1*450 = 450
  • 10*35 = 350
  • 50*10 = 500
  • 100*4 = 400
  • 400*1 = 400

Add up the products

450+350+500+400+400 = 2100

Then divide this over the total frequency (450+35+10+4+1 = 500)

So we get 2100/500 = 4.20 as the expected value.

4 0
2 years ago
PLEASE HELP!!!!!
Vadim26 [7]

Answer:

Step-by-step explanation:

9x - 1 / 2 + 9/2 x = 0.128886 (43)

2 / 5x - 1b = 4/3 - 1 - 1 = 2x (4)

= x1 + 24 - 3/4 + 8

9/3 - 1 x = /3

6 0
2 years ago
Answer pls I would really appreciate your help
tester [92]

Answer:

I think A

Step-by-step explanation:

srry if wrong

i hope this helps tho

3 0
2 years ago
The senior classes at High School A and High School B planned separate trips to Lake Compounce. The senior class at High School
storchak [24]

Answer:

Number of students in vans =15 and bus =46

Step-by-step explanation:

use variables for the vans and buses

let x= vans and y=buses

Now solve the 2 equations simultaneously

<em><u>remember</u></em><em><u> </u></em><em><u>to</u></em><em><u> </u></em><em><u>number</u></em><em><u> </u></em><em><u>your</u></em><em><u> </u></em><em><u>equations</u></em>

6x+7y=412..........1

6x+9y=504.........2

make x the subject of one equation

and label it equation 3

6x=412—7y

x =  \frac{206}{3}  -  \frac{7y}{6} .............3

subs 3 into 2

6( \frac{206}{3}  -  \frac{7y}{6} ) + 9y = 504

412 - 7y + 9y = 504

- 7y + 9y = 504 - 412

2y = 92

y = 46...................4

subs 4 into 1

6x + 7(46) = 412

6x + 322 = 412

6x = 412 - 322

6x = 90

x = 15

Therefore there are 15 students in each van and 46 students in each bus.

3 0
2 years ago
Jack's mother gave him 50 chocolates to give to his friends at his birthday party. He gave 3 chocolates to each of his friends a
Natasha_Volkova [10]

Answer:

16 friends

Step-by-step explanation:

Right at the beginning, you can take the 2 chocolates Jack was left with out of the 50 chocolates Jack had at the beginning. That equals 48 chocolate bars, so we know that Jack gave his friends a total if 48 chocolates

50 - 2 = 48

Now that you have the number 48, you are really close to the answer.

If you know that he gave each if his friends 3 chocolates, you can make that into an equation and put it into a calculator. That would look like this:

48 \div 3 = 16

The reason you do 48 ÷ 3 is because Jack divided his 48 chocolates into groups of 3 to give to each of the other kids.

You get the answer 16, which means the answer is 16 kids at his friend's birthday party.

3 0
3 years ago
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