Determine whether you can use the normal distribution to approximate the binomial distribution. If you can, use the normal distribution to approximate the indicated probabilities and sketch their graphs. If you cannot, explain why and use the binomial distribution to find the indicated probabilities.

A survey of adults in a region found that

58%

have encountered fraudulent charges on their credit cards. You randomly select

100

adults in the region. Complete parts (a) through (d) below.

Question content area bottom

Part 1

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

A.

No, because

nq<5.

B.

Yes, because both

np5

and

nq5.

C.

No, because

np<5.

Part 2

(a) Find the probability that the number who have encountered fraudulent charges on their credit cards is (a) exactly

60,

(b) at least

60,

and (c) fewer than

60.

enter your response here

(Round to four decimal places as needed.)

Part 3

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

A.

604175x

=58

A normal curve is over a horizontal axis and is centered on 58. Vertical line segments extend from the horizontal axis to the curve at 58 and 59.5. The area under the curve to the right of 59.5 is shaded.

B.

604175x

=58

A normal curve is over a horizontal axis and is centered on 58. Vertical line segments extend from the horizontal axis to the curve at 58, 59.5, and 60.5. The area under the curve between 59.5 and 60.5 is shaded.

C.

604175x

=58

A normal curve is over a horizontal axis and is centered on 58. Vertical line segments extend from the horizontal axis to the curve at 58 and 59.5. The area under the curve to the left of 59.5 is shaded.

D.

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

Part 4

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

60.

enter your response here

(Round to four decimal places as needed.)

Part 5

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

A.

604175x

=58

A normal curve is over a horizontal axis and is centered on 58. Vertical line segments extend from the horizontal axis to the curve at 58 and 59.5. The area under the curve to the left of 59.5 is shaded.

B.

604175x

=58

A normal curve is over a horizontal axis and is centered on 58. Vertical line segments extend from the horizontal axis to the curve at 58, 59.5, and 60.5. The area under the curve between 59.5 and 60.5 is shaded.

C.

604175x

=58

A normal curve is over a horizontal axis and is centered on 58. Vertical line segments extend from the horizontal axis to the curve at 58 and 59.5. The area under the curve to the right of 59.5 is shaded.

D.

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

Part 6

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

60.

enter your response here

(Round to four decimal places as needed.)

Part 7

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

A.

604175x

=58

A normal curve is over a horizontal axis and is centered on 58. Vertical line segments extend from the horizontal axis to the curve at 58 and 59.5. The area under the curve to the right of 59.5 is shaded.

B.

604175x

=58

A normal curve is over a horizontal axis and is centered on 58. Vertical line segments extend from the horizontal axis to the curve at 58 and 59.5. The area under the curve to the left of 59.5 is shaded.

C.

604175x

=58

A normal curve is over a horizontal axis and is centered on 58. Vertical line segments extend from the horizontal axis to the curve at 58, 59.5, and 60.5. The area under the curve between 59.5 and 60.5 is shaded.

D.

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

Part 8

(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 (b) is unusual because its probability is less than 0.05.

C.

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

D.

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