Question

In studies for a medication, 9 percent of patients gained weight as a side effect. Suppose 697 patients are randomly selected. Use the normal approximation to the binomial to approximate the probability that

(a) exactly 63 patients will gain weight as a side effect.

(b) no more than 63 patients will gain weight as a side effect.

(c) at least 77 patients will gain weight as a side effect. What does this result suggest?

Answer #1

X ~ Bin ( n , p)

Where n = 697 , p = 0.09

Using Normal Approximation to Binomial

Mean = n * P = ( 697 * 0.09 ) = 62.73

Variance = n * P * Q = ( 697 * 0.09 * 0.91 ) = 57.0843

Standard deviation = √(variance) = √(57.0843) = 7.5554

a)

With continuity correction

P(X = 63) = P(62.5 < X < 63.5)

P ( 62.5 < X < 63.5 ) = P ( Z < ( 63.5 - 62.73 ) /
7.5554 ) - P ( Z < ( 62.5 - 62.73 ) / 7.5554 )

= P ( Z < 0.1) - P ( Z < -0.03 )

= 0.5398 - 0.488

= **0.0518**

b)

With continuity correction

P(X <= 63) = P(X < 63.5)

P ( ( X < 63.5 ) = P ( Z < 63.5 - 62.73 ) / 7.5554 )

= P ( Z < 0.1 )

P ( X < 63.5 ) = **0.5398**

c)

With continuity correction

P(X >= 77) = P(X > 76.5)

P ( X > 76.5 ) = P(Z > (76.5 - 62.73 ) / 7.5554 )

= P ( Z > 1.82 )

= 1 - P ( Z < 1.82 )

= 1 - 0.9656

= **0.0344**

Since this probability is less than 0.05, the event is unusual.

In studies for a medication, 8 percent of patients gained
weight as a side effect. Suppose 498 patients are randomly
selected. Use the normal approximation to the binomial to
approximate the probability that (a) exactly 40 patients will gain
weight as a side effect. (b) no more than 40 patients will gain
weight as a side effect. (c) at least 50 patients will gain weight
as a side effect. What does this result suggest?

In studies for medication, 11 percent of patients gained weight
as a side effect. Suppose 402 patients are randomly selected. Use
the normal approximation to the binomial to approximate the
probability that
a) exactly 45 patients gain weight as a side effect
b) no more than 45 patients will gain weight as a side
effect
c) at least 53 patients will gain weight as a side effect. What
does this result suggest?

In studies for a medication, 88 percent of patients gained
weight as a side effect. Suppose 476 patients are randomly
selected. Use the normal approximation to the binomial to
approximate the probability that
(a) exactly 39 patients will gain weight as a side effect.
(Round to four decimal places as needed)
(b) no more than 39 patients will gain weight as a side effect.
(Round to four decimal places as needed)
(c) at least 48 patients will gain weight...

In studies for a medication, 4 percent of patients gained
weight as a side effect. Suppose 416 patients are randomly
selected. Use the normal approximation to the binomial to
approximate the probability that
(a) exactly 6 patients will gain weight as a side effect.
(b) 6 or fewer patients will gain weight as a side effect.
(c) 27 or more patients will gain weight as a side effect.
(d) between 6 and 14, inclusive, will gain weight as a side...

In studies for a medication,
66
percent of patients gained weight as a side effect. Suppose
465465
patients are randomly selected. Use the normal approximation to
the binomial to approximate the probability that
(a) exactly
1616
patients will gain weight as a side effect.
(b)
1616
or fewer patients will gain weight as a side effect.
(c)
3030
or more patients will gain weight as a side effect.
(d) between
1616
and
3838,
inclusive, will gain weight as a side...

In studies for a medication,
99
percent of patients gained weight as a side effect. Suppose
614614
patients are randomly selected. Use the normal approximation to
the binomial to approximate the probability that
(a) exactly
3939
patients will gain weight as a side effect.
(b)
3939
or fewer patients will gain weight as a side effect.
(c)
5858
or more patients will gain weight as a side effect.
(d) between
3939
and
4545,
inclusive, will gain weight as a side...

In studies for a medication, 9 percent of patients gained weight
as a side effect. Suppose 736 patients are randomly selected. Use
the normal approximation to the binomial to approximate the
probability that
(a) exactly 42 patients will gain weight as a side effect. __
(round to 4 decimal places as needed)
(b) 42 or fewer patients will gain weight as a side effect. __
(round to 4 decimal places as needed)
(c) 69 or more patients will gain weight...

In studies for a medication,14 percent of patients gained
weight as a side effect. Suppose 449 patients are randomly
selected. Use the normal approximation to the binomial to
approximate the probability that
(a) exactly 64 patients will gain weight as a side effect.
(b) 64 or fewer patients will gain weight as a side effect.
(c) 54 or more patients will gain weight as a side effect.
(d) between 64 and 86 inclusive, will gain weight as a side
effect.

In studies for a medication, 4 percent of patients gained
weight as a side effect. Suppose 749 patients are randomly
selected. Use the normal approximation to the binomial to
approximate the probability that (a) exactly 25 patients will gain
weight as a side effect. (b) 25 or fewer patients will gain weight
as a side effect. (c) 18 or more patients will gain weight as a
side effect. (d) between 25 and 37, inclusive, will gain weight
as a side...

In studies for a medication, 12 percent of patients gained
weight as a side effect. Suppose 492 patients are randomly
selected. Use the normal approximation to the binomial to
approximate the probability that (a) exactly 49 patients will gain
weight as a side effect. (b) 49 or fewer patients will gain weight
as a side effect. (c) 76 or more patients will gain weight as a
side effect. (d) between 49 and 75, inclusive, will gain weight
as a side...

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 7 minutes ago

asked 31 minutes ago

asked 34 minutes ago

asked 36 minutes ago

asked 37 minutes ago

asked 49 minutes ago

asked 53 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago