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

(a)Supposen=30andp=0.25.(For each answer, enter a number. Use 2 decimal places.)

np=

nq=

Can we approximatepby 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

npandnqdo not exceed

bothnpandnqexceed

npexceeds

npdoes not exceed

nqdoes not exceed

nqexceeds

fourth blank (Enter an exact number.)

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

_p=

mu sub p hat =

_p=

sigma sub p hat =

(b)Supposen= 25 andp= 0.15.Can we safely approximatepby 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

npandnqdo not exceed

bothnpandnqexceed

npexceeds

npdoes not exceed

nqdoes not exceed

nqexceeds

fourth blank (Enter an exact number.)

(c)Supposen=55andp=0.27.(For each answer, enter a number. Use 2 decimal places.)

np=

nq=

Can we approximatepby 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

npandnqdo not exceed

bothnpandnqexceed

npexceeds

npdoes not exceed

nqdoes not exceed

nqexceeds

fourth blank (Enter an exact number.)

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

_p=

mu sub p hat =

_p=

sigma sub p hat =