Quiz about Binomial / Normal Distribution

Question 1

If X follows a Binomial Distribution, P(X < 4) =

Accepted Answer

P( X $$\le$$ 3)

Answer

P( X $$\le$$ 4)

Answer

P( X $$\le$$ 5)

Question 2

If X follows a Binomial Distribution, P(X > 7) =

Accepted Answer

1 - P( X $$\le$$ 7)

Answer

1 - P( X $$\le$$ 6)

Answer

1 - P( X $$\le$$ 8)

Question 3

If X follows a Binomial Distribution, P(X $$\ge$$ 9) =

Accepted Answer

1 - P( X $$\le$$ 8)

Answer

1 - P( X $$\le$$ 9)

Answer

1 - P( X $$\le$$ 10)

Question 4

If X follows a Binomial Distribution, P( 8 $$\le$$ X $$\le$$ 15 ) =

Accepted Answer

P( X $$\le$$ 15) -

P( X $$\le$$ 7)

Answer

P( X $$\le$$ 15) -

P( X $$\le$$ 8)

Answer

P( X $$\le$$ 14) -

P( X $$\le$$ 8)

Answer

P( X $$\le$$ 14) -

P( X $$\le$$ 7)

Question 5

If X follows a Binomial Distribution, P( 11 < X < 23 ) =

Accepted Answer

P( X $$\le$$ 22) -

P( X $$\le$$ 11)

Answer

P( X $$\le$$ 23) -

P( X $$\le$$ 11)

Answer

P( X $$\le$$ 23) -

P( X $$\le$$ 10)

Answer

P( X $$\le$$ 22) -

P( X $$\le$$ 10)

Question 6

If X follows a Binomial Distribution, P( 27 $$\le$$ X $$<$$ 50 ) =

Accepted Answer

P( X $$\le$$ 49) -

P( X $$\le$$ 26)

Answer

P( X $$\le$$ 51) -

P( X $$\le$$ 26)

Answer

P( X $$\le$$ 50) -

P( X $$\le$$ 27)

Answer

P( X $$\le$$ 50) -

P( X $$\le$$ 26)

Answer

P( X $$\le$$ 49) -

P( X $$\le$$ 27)

Question 7

If X follows a Normal Distribution, P ( X < 25 ) =

(Hint: page 3 of notes)

Accepted Answer

P ( X $$\le$$ 25 )

Answer

P ( X $$\le$$ 24 )

Answer

P ( X $$\le$$ 26 )

Answer

1- P ( X $$\le$$ 25 )

Question 8

If X follows a Normal Distribution, P ( X $$\ge$$ 37 ) =

Accepted Answer

P ( X > 37 )

Answer

P ( X > 38 )

Answer

1- P ( X $$\le$$ 36 )

Question 9

The formula to perform standardization is

Accepted Answer

$$\frac{X-\mu}{\sigma^{ }}$$

Answer

$$\frac{X-\mu}{\sigma^2}$$

Answer

$$\frac{X-\sigma^2}{\mu}$$

Answer

$$\frac{X-\sigma^{ }}{\mu}$$

Question 10

When do we need to perform standardization ?

(You more choose more than one)

Accepted Answer

When mean is unknown

Accepted Answer

When variance is unknown

Answer

To find probabilities

Answer

Finding unknown when given probability

Answer

Actually there is no need for use of standardization since we have GC

Question 11

Let A ~ mass of a randomly chosen apple.

Let O ~ mass of a randomly chosen orange.

P( 2 randomly chosen apples exceed

twice the mass of a randomly chosen orange) =

Accepted Answer

$$P\left(A_1+A_2>2O\right)$$

Answer

$$P\left(2A>2O\right)$$

Answer

$$P\left(2A>O_1+O_2\right)$$

Answer

$$P\left(A_1+A_2>O_1+O_2\right)$$

Question 12

X~N(2,3)

What is $$X_1+X_2$$

(Hint: Page 11 of notes)

Accepted Answer

N(4,6)

Answer

N(4,12)

Answer

N(5,6)

Answer

N(5,12)

Question 13

X~N(2,3). What is 2X?

(Page 11 of notes)

Accepted Answer

N(4,12)

Answer

N(4,6)

Answer

N(5,6)

Answer

N(5,12)

Question 14

X~N(2,5) and Y~N(4,3)

X and Y are independent random variables.

What is Y-X?

Accepted Answer

N(2,8)

Answer

N(2,2)

Answer

N(2,-2)

Answer

N(-2,8)

Question 15

X~N(2,3) and Y~N(4,5)

X and Y are independent random variables.

What is $$3X-\left(Y_1+Y_2\right)$$ ?

Accepted Answer

(-2,37)

Answer

N(2,-1)

Answer

N(2,19)

Answer

N(2,37)

Question 16

Let X~height of a randomly chosen woman.

X~N(160, 4)

If, $$M=\frac{X_1+X_2+X_3+X_4}{4}$$ , M~ ?

(Hint: Page 13 of notes)

Accepted Answer

N(160,1)

Answer

N(160,4)

Answer

N(40,4)

Answer

N(40,1)

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