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

(a)

• Suppose n = 45 and
• p = 0.13.

(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

YesNo     

second blank

cancannot     

third blank

both n·p and n·qexceedn·p and n·q do notexceed     n·qexceedsn·q does not exceedn·pexceedsn·p does not exceed

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 = mu sub p hat =

σ_p̂ = 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. Ablank is represented by _____.)

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

first blank

YesNo     

second blank

cancannot     

third blank

both n·p and n·qexceedn·p and n·q do notexceed     n·qexceedsn·q does not exceedn·pexceedsn·p does not exceed

fourth blank (Enter an exact number.)

(c)

Suppose

• n = 59 and
• p = 0.40.

(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

YesNo     

second blank

cancannot     

third blank

both n·p and n·qexceedn·p and n·q do notexceed     n·qexceedsn·q does not exceedn·pexceedsn·p does not exceed

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 = mu sub p hat =

σ_p̂ = sigma sub p hat =