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

(a)

• Suppose n = 32 and
• p = 0.18.

(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

np does not exceed nq does not exceed np exceeds both np and nq exceed np and nq do not exceed nq exceeds

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 and
• p = 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

np does not exceed nq does not exceed np exceeds both np and nq exceed np and nq do not exceed nq exceeds

fourth blank (Enter an exact number.)

(c)

Suppose

• n = 49 and
• p = 0.29.

(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

np does not exceed nq does not exceed np exceeds both np and nq exceed np and nq do not exceed nq exceeds

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 =