Suppose we have a binomial experiment in which successis defined to be a particular quality or attribute that interestsus.

(a) Suppose n = 41 andp = 0.33.

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

Can we approximate p̂ by a normal distribution? Why? (Fillin the blank. There are four answer blanks. A blank is representedby _____.)

_____, p̂ _____ be approximated by a normal randomvariable because _____ _____.

first blank:

Yes or No    

second blank:

can or cannot    

third blank:

n·q does not exceed

both n·p and n·qexceed    

n·p exceeds

n·p and n·q do notexceed

n·p does not exceed

n·q exceeds

fourth blank (Enter an exact number.)
________

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

σ_p̂ =

(b) Suppose n = 25 andp = 0.15.

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

_____, p̂ _____ be approximated by a normal randomvariable because _____ _____.

first blank:

Yes or No    

second blank:

can or cannot    

third blank:

n·q does not exceed

both n·p and n·qexceed   

n·p exceeds

n·p and n·q do notexceed

n·p does not exceed

n·q exceeds

fourth blank (Enter an exact number.):
________

(c) Suppose n =48 and p = 0.11.

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

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

_____, p̂ _____ be approximated by a normal randomvariable because _____ _____.

first blank

Yes or No    

second blank

can or cannot    

third blank

n·q does not exceed

both n·p and n·qexceed   

n·p exceeds

n·p and n·q do notexceed

n·p does not exceed

n·q exceeds

fourth blank (Enter an exact number.)
_______

What are the values of μ_p̂ andσ_p̂? (For each answer, enter a number.Use 3 decimal places.)
μ_p̂ =
σ_p̂ =