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 53% have encountered fraudulent charges on their credit cards. You randomly select 100 adults in the region. Complete parts (a) through (d) below.
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Part 1
Determine whether a normal distribution can be used to approximate the binomial distribution. Choose the correct answer below.
A.
Yes, because both npgreater than or equals5 and nqgreater than or equals5.
Your answer is correct.B.
No, because npless than5.
C.
No, because nqless than5.
Part 2
(a) Find the probability that the number who have encountered fraudulent charges on their credit cards is (a) exactly 55, (b) at least 55, and (c) fewer than 55.
. 0736 (Round to four decimal places as needed.)
Part 3
Sketch the graph of the normal distribution with the indicated probability shaded.
A.
55
36
70
x
mu equals 53
A normal curve is over a horizontal axis and is centered on 53. Vertical line segments extend from the horizontal axis to the curve at 53, 54.5, and 55.5. The area under the curve between 54.5 and 55.5 is shaded.
Your answer is correct.B.
55
36
70
x
mu equals 53
A normal curve is over a horizontal axis and is centered on 53. Vertical line segments extend from the horizontal axis to the curve at 53 and 54.5. The area under the curve to the right of 54.5 is shaded.
C.
55
36
70
x
mu equals 53
A normal curve is over a horizontal axis and is centered on 53. Vertical line segments extend from the horizontal axis to the curve at 53 and 54.5. The area under the curve to the left of 54.5 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 55.
select: .6179
. 6179 (Round to four decimal places as needed.)
