Q1) You take multiple choice test made up questions.Each question has 4 possible

Question

Q1) You take multiple choice test made up questions.Each question has 4 possible answers.how many different ways are there to answer the test(assuming you don't leave a question blank)?

Q2) In bolt factory machines m1,m2,m3 manufacture respectively 25,35, and 40 percent of the total output. of their output 5,4, and 2 percent respectively are defective bolts.one bolt is drawn at random from the product and is found to be defective, what is the probablity that it is manufactured in the machine m2?

Q3) There are 6 bulbs in a house out which 3 are defective .If 2 bulbs are picked randomly,find the probablity that at most one is defective.what is the average defective bulbs ?

Q4) Customers arrive at a store at the rate of 10 per hour,

(a) what is the probablity that at least 2 hours .

(b) find the probablity taht no customer will arrive for first half an hour.

Q5) A company receives on average 75 couriers with a standard deviation of 5 in a week.what percentage of the data set lies between 50 and 100?

Q6) 62% of 12th graders attend school in a particular urban school district.A sample of 50 children are selected .Use normal approximation to find the probablity that less than 20 are actually enrolledin school.F(-3.35)=.0004

Q7) Suppose you are waiting at the airport to recieve your friendand flight is expected to landin another 20 minutes. by using uniform distribution find the probabblity that teh flight lands in between now and the next 10 minutes?

Q8) Let teh random variables X and Y have joint probablity density function

f(x,y)=c(x2y+xy) ; 0<x<1,0<y<1

(a) find the value of 'c' that makes function a joint density.

(b) Compoute E(Y)

Explanation / Answer

2)
Let E be the probability of drawing defective bolt.
Let E1, E2 and E3 be the event of drawing a bolt produced by the Machines A, B and C respectively.
Then ,
P(E1) = 25/100, P(E2) = 35/100, P(E3) = 40/100,
P(E/E1) = 5/100, P(E/E2) = 4/100, P(E/E3) = 2/100.

Therefore, P(E2/E) = [P(E2).P(E/E2)]/[P(E1).P(E/E1) + P(E2).P(E/E2) + P(E3).P(E/E3)]
= [(35/100)(4/100)]/[(25/100)(5/100) + (35/100)(4/100) + (40/100)(2/100)]
= [35*4]/[25*5 + 35*4 + 40*2]
= 140/(125 + 140 + 80)
= 140/345
= 28/69

3)

Number of ways in which 2 bulbs can be selected from 6 components = 6C2

P [no bulbs are defective]= 3C2 / 6C2

P [only one bulb is defective]= = 3C1 * 3C1 / 6C2

Required probability = P [no bulbs are defective] + P [only one bulbs are defective]
= 3/15 + 9/15 = 12/15

5)
mean =75 , s = 5
P(50 < x < 100)
= P((50 - 75) /5 < z < ( 100-75) /5)
= P(-5 < z < 5)
P(50 < x < 100) = P(-5 < z < 5) = 1

6)
n = 50 , p = 0.62 , q = 0.38
mean = np = 50 *0.38= 31
std. dev = sqrt(npq)
= sqrt(50*0.62*0.38)
= 3.4322
P(X<20)
z = (x - mean)/s
= (20 - 31)/3.4322
= -3.2049
P(X<20) = P(z <-3.2049) = 0.0007

7)
The interval of the probability distribution in minutes is [0, 20].

And the probability density is 1/20–0 = 120.

You wish your friend to land within next 10 minutes. That is, the sub interval of the successful event is [0, 10].

Now the probability P ( x < 10) is the ratio of the widths of these two intervals.

=> 10/20=12.

Hence the probability of the flight landing within 5 minutes is 1 /2.

Related Questions

Navigate

• Browse (All)
• Browse Q
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.