Determine whether you can use the normal distribution to approximate the binomial distribution. If youcan, use the normal distribution to approximate the indicated probabilities and sketch their graphs. If youcannot, explain why and use the binomial distribution to find the indicated probabilities.

A survey of adults in a region found that 54% have encountered fraudulent charges on their credit cards. You randomly select 100 adults in the region. Complete parts(a) through(d) below.

Determine whether a normal distribution can be used to approximate the binomial distribution. Choose the correct answer below.

A.

No, because np<5.

B.

Yes, because both np5 and nq5.

C.

No, because nq<5.

(a) Find the probability that the number who have encountered fraudulent charges on their credit cards is(a) exactly 57, (b) at least 57, and(c) fewer than 57.

nothing

(Round to four decimal places asneeded.)

Sketch the graph of the normal distribution with the indicated probability shaded.

A.

57

37

71

x

=54

A normal curve is over a horizontal axis and is centered on 54. Vertical line segments extend from the horizontal axis to the curve at 54, 56.5, and 57.5. The area under the curve between 56.5 and 57.5 is shaded.

B.

57

37

71

x

=54

A normal curve is over a horizontal axis and is centered on 54. Vertical line segments extend from the horizontal axis to the curve at 54 and 56.5. The area under the curve to the left of 56.5 is shaded.

C.

57

37

71

x

=54

A normal curve is over a horizontal axis and is centered on 54. Vertical line segments extend from the horizontal axis to the curve at 54 and 56.5. The area under the curve to the right of 56.5 is shaded.

D.

The normal distribution cannot be used to approximate the binomial distribution.

(b) Find the probability that the number who have encountered fraudulent charges on their credit cards is at least 57.

nothing

(Round to four decimal places asneeded.)

Sketch the graph of the normal distribution with the indicated probability shaded.

A.

57

37

71

x

=54

A normal curve is over a horizontal axis and is centered on 54. Vertical line segments extend from the horizontal axis to the curve at 54 and 56.5. The area under the curve to the left of 56.5 is shaded.

B.

57

37

71

x

=54

A normal curve is over a horizontal axis and is centered on 54. Vertical line segments extend from the horizontal axis to the curve at 54, 56.5, and 57.5. The area under the curve between 56.5 and 57.5 is shaded.

C.

57

37

71

x

=54

A normal curve is over a horizontal axis and is centered on 54. Vertical line segments extend from the horizontal axis to the curve at 54 and 56.5. The area under the curve to the right of 56.5 is shaded.

D.

The normal distribution cannot be used to approximate the binomial distribution.

(c) Find the probability that the number who have encountered fraudulent charges on their credit cards is fewer than 57.

nothing

(Round to four decimal places asneeded.)

Sketch the graph of the normal distribution with the indicated probability shaded.

A.

57

37

71

x

=54

A normal curve is over a horizontal axis and is centered on 54. Vertical line segments extend from the horizontal axis to the curve at 54 and 56.5. The area under the curve to the right of 56.5 is shaded.

B.

57

37

71

x

=54

A normal curve is over a horizontal axis and is centered on 54. Vertical line segments extend from the horizontal axis to the curve at 54 and 56.5. The area under the curve to the left of 56.5 is shaded.

C.

57

37

71

x

=54

A normal curve is over a horizontal axis and is centered on 54. Vertical line segments extend from the horizontal axis to the curve at 54, 56.5, and 57.5. The area under the curve between 56.5 and 57.5 is shaded.

D.

The normal distribution cannot be used to approximate the binomial distribution.

(d) Identify any unusual events. Explain.

A.

The event in part(c) is unusual because its probability is less than 0.05.

B.

The event in part(a) is unusual because its probability is less than 0.05.

C.

The event in part(b) is unusual because its probability is less than 0.05.

D.

There are no unusualevents, because all of the probabilities are greater than 0.05.

Click to select your answer(s).