Compute P(X) using the binomial probability formula. Then determine whether the normal distribution can be used to estimate this probability. If so, approximate P(X) using the normal distribution and compare the result with the exact probability.
n
=
59, p
=
0.3, and X
=
24
Question content area bottom
Part 1
For n
=
59, p
=
0.3, and X
=
24, find P(X).
P(X)
=
enter your response here
(Round to four decimal places as needed.)
Part 2
Can the normal distribution be used to approximate this probability?
A.
No, the normal distribution cannot be used because
np(1−p)≥10.
B.
Yes, the normal distribution can be used because
np(1−p)≤10.
C.
Yes, the normal distribution can be used because
np(1−p)≥10.
D.
No, the normal distribution cannot be used because
np(1−p)<10.
Part 3
Approximate P(X) using the normal distribution. Select the correct choice below and fill in any answer boxes in your choice.
A.
P(X)
=
enter your response here
(Round to four decimal places as needed.)
B.
The normal distribution cannot be used.
Part 4
By how much do the exact and approximated probabilities differ? Select the correct choice below and fill in any answer boxes in your choice.
