(a) Suppose n = 43 and p = 0.27. (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 is represented by _____.)

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

first blank

Yes

No     

second blank

can

cannot     

third blank

n·p exceeds

both n·p and n·q exceed     

n·p and n·q do not exceed

n·q exceeds

n·q does not exceed

n·p does not exceed

fourth blank (Enter an exact number.)

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

μp̂ = 

mu sub p hat =

σp̂ = 

sigma sub p hat =

(b) Suppose n = 25 and p = 0.15. Can we safely approximate p̂ by a normal distribution? Why or why not? (Fill in the blank. There are four answer blanks. A blank is represented by _____.)

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

first blank

Yes

No     

second blank

can

cannot 

third blank

n·p exceeds

both n·p and n·q exceed     

n·p and n·q do not exceed

n·q exceeds

n·q does not exceed

n·p does not exceed

fourth blank (Enter an exact number.)

(c) Suppose n = 64 and p = 0.26. (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 is represented by _____.)

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

first blank

Yes

No     

second blank

can

cannot     

third blank

n·p exceeds

both n·p and n·q exceed     

n·p and n·q do not exceed

n·q exceeds

n·q does not exceed

n·p does not exceed

fourth blank (Enter an exact number.)

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

μp̂ = 

mu sub p hat =

σp̂ = 

sigma sub p hat =