Question 841623: A coin is weighted so that heads is twice as likely to appear as tails.
a) What is the probability that one will get more than five heads if ten such coins are tossed?
b)In a school, students are admitted through an interview scores are assumed to follow a normal distribution as X->N (45,100)
I)find the probability that a randomly selected student will score between 40 and 60
ii)If 100 students take the test and the school needs to take 40 students,what should the pass mark be?
iii)explain the limitation of using these statistical limitations for admitting students.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! A coin is weighted so that heads is twice as likely to appear as tails.
P(heads) = 3/4 ; p(tails) = 1/3
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a) What is the probability that one will get more than five heads if ten such coins are tossed?
Ans: P(6<= x <=10) = 1 - binomcdf(10,3/4,5) = 0.9219
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b)In a school, students are admitted through an interview scores are assumed to follow a normal distribution as X->N (45,100)
I)find the probability that a randomly selected student will score between 40 and 60
z(40) = (40-45)/100 = -5/100 = -1/20
z(60) = (60-45)/100 = 15/100 = 3/20
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P(40<= x <= 60) = P(-1/20<= z <=3/20) = normalcdf(-1/20,3/20) = 0.0796
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ii)If 100 students take the test and the school needs to take 40 students,what should the pass mark be?
z(60) = 3/20
score = (3/20)*100+45 = 60
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iii)explain the limitation of using these statistical limitations for admitting students.
I'll leave that to you.
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Cheers,
Stan H.
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