Question

In: Statistics and Probability

Suppose we have a binomial experiment in which success is defined to be a particular quality...

Suppose we have a binomial experiment in which success is defined to be a particular quality or attribute that interests us.

(a) Suppose n = 43 and p = 0.36.

(For each answer, enter a number. Use 2 decimal places.)
n·p =
n·q =

Can we approximate by a normal distribution? Why? (Fill in the blank. There are four answer blanks. A blank is represented by _____.)

_____, _____ be approximated by a normal random variable because _____ _____.

first blank

Yes or No    

second blank

can or cannot    

third blank

n·p exceeds

n·p and n·q do not exceed    

n·q exceeds

n·p does not exceed

n·q does not exceed

both n·p and n·q exceed

fourth blank (Enter an exact number.)
__________

What are the values of μ and σ? (For each answer, enter a number. Use 3 decimal places.)
μ =

σ =

(b) Suppose n = 25 and p = 0.15.

Can we safely approximate by a normal distribution? Why or why not? (Fill in the blank. There are four answer blanks. A blank is represented by _____.)

_____, _____ be approximated by a normal random variable because _____ _____.

first blank

Yes or No    

second blank

can or cannot    

third blank

n·p exceeds

n·p and n·q do not exceed    

n·q exceeds

n·p does not exceed

n·q does not exceed

both n·p and n·q exceed

fourth blank (Enter an exact number.)
_____

(c) Suppose n = 56 and p = 0.19.

(For each answer, enter a number. Use 2 decimal places.)
n·p =
n·q =

Can we approximate by a normal distribution? Why? (Fill in the blank. There are four answer blanks. A blank is represented by _____.)

_____, _____ be approximated by a normal random variable because _____ _____.

first blank

Yes or No    

second blank

can or cannot    

third blank

n·p exceeds

n·p and n·q do not exceed   

n·q exceeds

n·p does not exceed

n·q does not exceed

both n·p and n·q exceed

fourth blank (Enter an exact number.)

_____
What are the values of μ and σ? (For each answer, enter a number. Use 3 decimal places.)
μ =

σ =

Solutions

Expert Solution

, be approximated by a normal random variable because

, be approximated by a normal random variable because

, be approximated by a normal random variable because


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