Question

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

(a)

- Suppose
*n*= 42 and *p*= 0.30.

(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 or No

second blank

can or cannot

third blank

*n*·*q* does not exceed

both *n*·*p* and *n*·*q*
exceed

*n*·*p* and *n*·*q* do not
exceed

*n*·*p* exceeds

*n*·*p* does not exceed

*n*·*q* exceeds

fourth blank (Enter an exact number.)

What are the values of *μ*_{p̂} and
*σ*_{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. A
blank is represented by _____.)

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

first blank

Yes or No

second blank

can or cannot

third blank

*n*·*q* does not exceed

both *n*·*p* and *n*·*q*
exceed

*n*·*p* and *n*·*q* do not
exceed

*n*·*p* exceeds

*n*·*p* does not exceed

*n*·*q* exceeds

fourth blank (Enter an exact number.)

(c)

Suppose

*n*= 56 and*p*= 0.19.

(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 or No

second blank

can or cannot

third blank

*n*·*q* does not exceed

both *n*·*p* and *n*·*q*
exceed

*n*·*p* and *n*·*q* do not
exceed

*n*·*p* exceeds

*n*·*p* does not exceed

*n*·*q* exceeds

fourth blank (Enter an exact number.)

What are the values of *μ*_{p̂} and
*σ*_{p̂}? (For each answer, enter a number.
Use 3 decimal places.)

*μ*_{p̂} = mu sub p hat =

*σ*_{p̂} = sigma sub p hat =

Answer #1

(a) n = 42, p = 0.30

n.p = 12.6

n.q = 29.4

Yes, can be approximated by a normal random variable because both n.p and n q exceed 5

= np = 12.6

= \sqrt{npq} = 2.970

(b) n = 25, p = 0.15

n.p = 3.75

n.q = 21.25

No, cannot be approximated by a normal random variable because n.p does not exceed 5

(c) n = 56, p = 0.19

n.p = 10.64

n.q = 45.36

Yes, can be approximated by a normal random variable because both n.p and n.q exceed 5

= np = 10.64

= \sqrt{npq} = 2.936

Suppose we have a binomial experiment in which success
is defined to be a particular quality or attribute that interests
us.
(a)
Suppose n = 31 and p =
0.20.
(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 _____...

Suppose we have a binomial experiment in which success is
defined to be a particular quality or attribute that interests
us.
(a)
Suppose n = 35 and
p = 0.37.
(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 _____...

Suppose we have a binomial experiment in which success is
defined to be a particular quality or attribute that interests us.
(a) Suppose n = 28 and p = 0.37. (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 _____...

Suppose we have a binomial experiment in which success is
defined to be a particular quality or attribute that interests us.
(a) Suppose n = 28 and p = 0.29. (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 _____...

Suppose we have a binomial experiment in which success
is defined to be a particular quality or attribute that interests
us.
(a) Suppose n = 42 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 is
represented by _____.)
_____, p̂ _____ be approximated by a normal random
variable because _____...

Suppose we have a binomial experiment in which success is
defined to be a particular quality or attribute that interests
us.
(a) Suppose n = 39 and p = 0.23. (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 _____...

Suppose we have a binomial experiment in which success is
defined to be a particular quality or attribute that interests us.
(a) Suppose n = 34 and p = 0.25. (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 _____...

Suppose we have a binomial experiment in which success is
defined to be a particular quality or attribute that interests
us.
(a) Suppose n = 35 and p = 0.33. (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 _____...

Suppose we have a binomial experiment in which success is
defined to be a particular quality or attribute that interests
us.
(a) Suppose n = 30 and p = 0.20. (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 _____...

Suppose we have a binomial experiment in which success is
defined to be a particular quality or attribute that interests
us.
(a)
Suppose n = 45 and
p = 0.38.
(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 _____...

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