Question

A certain flight arrives on time 90 percent of the time. Suppose 184 flights are randomly selected. Use the normal approximation to the binomial to approximate the probability that

(a) exactly 174 flights are on time. (Round to four decimal places as needed.)

(b) at least 174 flights are on time. (Round to four decimal places as needed.)

(c) fewer than 170 flights are on time. (Round to four decimal places as needed.)

(d) between 170 and 177, inclusive are on time. (Round to four decimal places as needed.)

Answer #1

a)

Mean = n p = 184 * 0.90 = 165.6

Standard deviation = sqrt [ n p (1 - p) ]

= sqrt ( 184 * 0.90 * ( 1 - 0.90) ]

= 4.0694

Using normal approximation,

P(X < x) = P( Z < ( X - mean ) / SD )

P(X = 174) = P ( 173.5 < X < 174.5 ) (With
continuity correction )

P ( 173.5 < X < 174.5 ) = P ( Z < ( 174.5 - 165.6 ) /
4.0694 ) - P ( Z < ( 173.5 - 165.6 ) / 4.0694 )

= P ( Z < 2.19) - P ( Z < 1.94 )

= 0.9857 - 0.9738

= **0.0119**

b)

X ~ N ( µ = 165.6 , σ = 4.0694 )

We covert this to standard normal as

P ( X < x) = P ( (Z < X - µ ) / σ )

P(X >= 174) = P(X > 173.5 ) With continuity correction
)

P ( X > 173.5 ) = P(Z > (173.5 - 165.6 ) / 4.0694 )

= P ( Z > 1.94 )

= 1 - P ( Z < 1.94 )

= 1 - 0.9738

= **0.0262**

c)

P(X < 170)= P(X < 169.5) (With continuity correction )

P ( ( X < 169.5 ) = P ( Z < 169.5 - 165.6 ) / 4.0694
)

= P ( Z < 0.96 )

P ( X < 169.5 ) = **0.8315**

d)

P(170 < X < 177) = P(169.5 < X < 177.5) (With continuity correction )

P ( 169.5 < X < 177.5 ) = P ( Z < ( 177.5 - 165.6 ) /
4.0694 ) - P ( Z < ( 169.5 - 165.6 ) / 4.0694 )

= P ( Z < 2.92) - P ( Z < 0.96 )

= 0.9982 - 0.8315

= **0.1668**

A certain flight arrives on time 90 percent of the time. Suppose
166 flights are randomly selected. Use the normal approximation to
the binomial to approximate the probability that (a) exactly 146
flights are on time. (b) at least 146 flights are on time. (c)
fewer than 139 flights are on time. (d) between 139 and 158,
inclusive are on time.

A certain flight arrives on time 90 percent of the time. Suppose
190 flights are randomly selected. Use the normal approximation to
the binomial to approximate the probability that
(a) exactly 163 flights are on time.
(b) at least 163 flights are on time.
(c) fewer than 182 flights are on time.
(d) between 182 and 183, inclusive are on time.

A certain flight arrives on time 81 percent of the time. Suppose
122 flights are randomly selected. Use the normal approximation to
the binomial to approximate the probability that
(a) exactly 110 flights are on time.
(b) at least 110 flights are on time.
(c) fewer than 110 flights are on time.
(d) between 110 and 111, inclusive are on time.

A certain flight arrives on time
83 percent of the time. Suppose 130 flights are randomly
selected. Use the normal approximation to the binomial to
approximate the probability that
(a) exactly 117 flights are on time.
(b) at least 117
flights are on time.
(c) fewer than 96 flights are on time.
(d) between 96 and 108, inclusive are on time.

A certain flight arrives on time 85 percent of the time. Suppose
188 flights are randomly selected. Use the normal approximation to
the binomial to approximate the probability that (a) exactly 160
flights are on time. (b) at least 160 flights are on time. (c)
fewer than 155 flights are on time. (d) between 155 and 166,
inclusive are on time.

A certain flight arrives on time
81
percent of the time. Suppose
113
flights are randomly selected. Use the normal approximation to
the binomial to approximate the probability that
(a) exactly
89
flights are on time.
(b) at least
89
flights are on time.
(c) fewer than
87
flights are on time.
(d) between
87
and
97
,
inclusive are on time.

A certain flight arrives on time 89 percent of the time. Suppose
118 flights are randomly selected. Use the normal approximation to
the binomial to approximate the probability that
(a) exactly 95 flights are on time.
(b) at least 95 flights are on time.
c) fewer than 107 flights are on time.
(d) between 107 and 108, inclusive are on time.

A certain flight arrives on time 89 percent of the time. Suppose
135 flights are randomly selected. Use the normal approximation to
the binomial to approximate the probability that (a) exactly 127
flights are on time. (b) at least 127 flights are on time. (c)
fewer than 117 flights are on time. (d) between 117 and 129,
inclusive are on time.

A certain flight arrives on time 88 percent of the time. Suppose
183 flights are randomly selected. Use the normal approximation to
the binomial to approximate the probability that
(a) exactly 147 flights are on time.
(b) at least 147 flights are on time.
(c) fewer than 166 flights are on time.
(d) between 166 and 173, inclusive are on time.

A certain flight arrives on time 86 percent of the time. Suppose
112 flights are randomly selected. Use the normal approximation to
the binomial to approximate the probability that
(a) exactly 100 flights are on time.
(b) at least 100 flights are on time.
(c) fewer than 99 flights are on time.
(d) between 99 and 106, inclusive are on time.

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 37 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 2 hours ago

asked 2 hours ago

asked 2 hours ago

asked 2 hours ago

asked 2 hours ago