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]
3 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]3 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
Simplify the following expression: (−3)(−2)( −2)<br> A −12<br> B 12<br> C −18<br> D 18
nydimaria [60]
A -12 Hope this helps
7 0
3 years ago
Read 2 more answers
Can anyone help? I’m having trouble.
andrew11 [14]

Answer:

I think it's around 9.8 or something

Step-by-step explanation:

sqrt(100) is 10

so the sqrt(95) should be around 9.8

6 0
3 years ago
PLEASE HELP 25PT
Bess [88]
Hi


1.If Mrs.Walters drives 360 miles on 25 gallons of gas , she drives 14.4 miles on 1 gallon of gas .

Work; I made a proportion , but you can just divide 360 and 25 .
 x=14.4 miles

If Mr.Walters drives 480 miles on 32 gallons of gas , he drives 15.06 miles on 1 gallon of gas .
 x=15.06 miles
2. Mr.Walter because he drives more miles with a gallon .
Work; 15.06 miles is greater than 14.4 miles.

Hope it helps and have a wonderful day.
7 0
3 years ago
Verifying Properties of logarithms In Exercise,use a graphing utility to verify that the functions are equivalent for x &gt; 0.
Ede4ka [16]

Answer:

Applying Quotient and power rule. Graphically, for x>0 both curves coincide.

Step-by-step explanation:

1) Firstly, by applying the Quotient and then the Power Rule, we have a subtraction of the argument and, finally the exponent turns to be the coefficient. As it follows:

lnx=log_{e}x\\\\f(x) = ln({\frac{x^{2}}{4}})\Rightarrow f(x)=ln{x^2}-ln4\Rightarrow f(x)=2lnx-ln4\\g(x) = 2 ln x - ln 4

2) Check the graph below to see this equivalence. to see x>0 they  both coincide.

7 0
3 years ago
Without solving. what value for n makes this equation true?​
Pavel [41]

Answer:

52

Step-by-step explanation:

n + 94 = 32 + 114

n + 94 = 146

n = 146 - 94

n = 52

<h3>Hope it is helpful...</h3>
5 0
3 years ago
Other questions:
  • Q - 2q &gt; 32 What is q?
    15·1 answer
  • Which statements are true about car color? Choose four correct answers. White is the most popular in every region. Red is the mo
    12·2 answers
  • Evaluate : <br> \(\cos 12 \cos 24 \cos 36 \cos 48 \cos 72 \cos 84\)
    11·1 answer
  • Are 21q-7q and (3q-p)(7) equivalent
    12·1 answer
  • In the number 252 the 2 in the ones place is ____the value of the 2 in the hundreds place
    10·1 answer
  • What's the smallest number divisible by 1-11?
    9·1 answer
  • Write an equation of the line with the given slope and y-intercept.<br> slope:1/9, y-intercept: 3
    14·1 answer
  • What are the steps in solving<br> 12x+4=20x+24
    5·2 answers
  • Christian is training for a swimming competition He starts swimming 10 ft. from the shore to his boat The table below represents
    9·2 answers
  • What’s the area of this following circle?
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!