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

(a) Suppose n = 44 andp = 0.26.(For each answer, enter a number. Use 2 decimal places.)

np =

nq =

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

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

first blank

Yes

No

second blank

can

cannot

third blank

nq does not exceed

np does not exceed

np exceeds

both np and nq exceed

nq exceeds

np and nq do not exceed

fourth blank (Enter an exact number.)

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

p = mu sub p hat =

p = sigma sub p hat =

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

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

first blank

Yes

No

second blank

can

cannot

third blank

nq does not exceed

np does not exceed

np exceeds

both np and nq exceed

nq exceeds

np and nq do not exceed

fourth blank (Enter an exact number.)

(c) Suppose n = 52 andp = 0.37.(For each answer, enter a number. Use 2 decimal places.)

np =

nq =

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

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

first blank

Yes

No

second blank

can

cannot

third blank

nq does not exceed

np does not exceed

np exceeds

both np and nq exceed

nq exceeds

np and nq do not exceed

fourth blank (Enter an exact number.)

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

p = mu sub p hat =

p = sigma sub p hat =