1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Reptile [31]
2 years ago
13

The University of Washington claims that it graduates 85% of its basketball players. An NCAA investigation about the graduation

rate finds that of the last 20 players entering the program only 11 graduated. If the university’s claim is correct, the number of players among the 20 should follow the binomial distribution B(20, 0.85).
a) What is the probability that 11 out of the 20 would graduate? Write how the binomial formula is used to calculate the probability.

(Answer: 0.74%) ?

b) To what extent do you think the university’s claim is true?

(Answer: Very low extent) ?

c) What is the probability that all 20 athletes would have graduated? Write how the binomial formula is used to calculate the probability.

(Answer: 3.86%) ?

d) Find the mean and standard deviation of the number of graduates out of the 20 players.
Mathematics
1 answer:
Nonamiya [84]2 years ago
8 0

Probabilities are used to determine the chances of events

The given parameters are:

  • Sample size: n = 20
  • Proportion: p = 85%

<h3>(a) What is the probability that 11 out of the 20 would graduate? </h3>

Using the binomial probability formula, we have:

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

So, the equation becomes

P(x = 11) = ^{20}C_{11} \times (85\%)^{11} \times (1 - 85\%)^{20 -11}    

This gives

P(x = 11) = 167960 \times (0.85)^{11} \times 0.15^{9}

P(x = 11) = 0.0011

Express as percentage

P(x = 11) = 0.11\%

Hence, the probability that 11 out of the 20 would graduate is 0.11%

<h3>(b) To what extent do you think the university’s claim is true?</h3>

The probability 0.11% is less than 50%.

Hence, the extent that the university’s claim is true is very low

<h3>(c) What is the probability that all  20 would graduate? </h3>

Using the binomial probability formula, we have:

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

So, the equation becomes

P(x = 20) = ^{20}C_{20} \times (85\%)^{20} \times (1 - 85\%)^{20 -20}    

This gives

P(x = 20) = 1 \times (0.85)^{20} \times (0.15\%)^0

P(x = 20) = 0.0388

Express as percentage

P(x = 20) = 3.88\%

Hence, the probability that all 20 would graduate is 3.88%

<h3>(d) The mean and the standard deviation</h3>

The mean is calculated as:

\mu = np

So, we have:

\mu = 20 \times 85\%

\mu = 17

The standard deviation is calculated as:

\sigma = np(1 - p)

So, we have:

\sigma = 20 \times 85\% \times (1 - 85\%)

\sigma = 20 \times 0.85 \times 0.15

\sigma = 2.55

Hence, the mean and the standard deviation are 17 and 2.55, respectively.

Read more about probabilities at:

brainly.com/question/15246027

You might be interested in
How do I simplify the question in the red boy
Leni [432]
Divide them and youll get your answer
7 0
2 years ago
Read 2 more answers
How many time does 8 go into 27
iogann1982 [59]
It is: 27/8 = 3 with a remainder of 3


4 0
3 years ago
Read 2 more answers
What is the commutative property for 4xy <br> PLEASE ANSWER QUICKLY
ValentinkaMS [17]

Answer:

we \: know \: that \: commutative \: prop  \\  = x + y = y + x \\ then \\ 4xy + 0 = 0 + 4xy \\ thank \: you

7 0
2 years ago
A function is _____ a relation. <br><br> A) always <br> B) sometimes <br> C) never
VikaD [51]
I believe that; A function is {A) sometimes} a relation.
4 0
3 years ago
Find the slope of the line​
Sergio039 [100]

Answer:

A) 2

Step-by-step explanation:

4 0
2 years ago
Read 2 more answers
Other questions:
  • Paul’s dog weighs 12 pounds more that Issac’s dog. Together they weigh 50 pounds. How much does Issac dog weigh ???
    13·1 answer
  • I need answer ASAP !:/
    5·1 answer
  • If the total price of a sofa is $660, including a tax of 0.08 times the list price,what is the list price of the sofa (to the ne
    15·2 answers
  • 11) The sum of two numbers is 25. The difference of two numbers is 3.
    6·1 answer
  • A line with a slope of -2 passes through the point (-2, -1). What is its equation in slope-intercept form?
    15·1 answer
  • The final velocity of an object moving in one dimension is given by the formula v = u + at, where u is the initial velocity, a i
    12·2 answers
  • Which expression is not equivalent to 3x-2
    8·1 answer
  • I need help!!! Can someone answer this? It’s very simple!
    6·1 answer
  • Find the factors pairs of 78
    10·2 answers
  • Hi, can you help me answer this question please, thank you!
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!