Question

A binomial distribution has p? = 0.26 and n? = 76. Use the
normal approximation to the binomial distribution to answer parts
?(a) through ?(d) below.

?a) What are the mean and standard deviation for this?
distribution?

?b) What is the probability of exactly 15 ?successes?

?c) What is the probability of 14 to 23 ?successes?

?d) What is the probability of 11 to 18 ?successes

Answer #1

We have given , p=0.26 , n=76

a) Mean =

standard deviation

?b) the probability of exactly 15 ?successes

P[X=15]

=P[15-0.5<X<15+0.5]

=P[14.5<X<15.5]

=P[-1.38<Z<-1.11]

=0.1335-0.0838..........................by using normal probability table.

=0.0497

?c) the probability of 14 to 23 ?successes

P[14<X<23]

=P[14.5<X<22.5]...................using continuity correction

=P[-1.38<Z<0.72]

=0.7642-0.0838.........................................by using normal probability table

=0.6804

?d) the probability of 11 to 18 ?successes

P[11<X<18]

=P[11.5<X<17.5]...........................by using continuity correction

=P[-2.16<Z<-0.59]

=0.2776-0.0154.......................by using normal probability table.

=0.2622

A binomial probability distribution has p = 0.20 and n =
100.
(d) What is the probability of 17 to 23 successes? Use the
normal approximation of the binomial distribution to answer this
question. (Round your answer to four decimal places.)
(e) What is the probability of 14 or fewer successes? Use the
normal approximation of the binomial distribution to answer this
question. (Round your answer to four decimal places.)

A binomial distribution has p=0.64 and n=25.
a. What are the mean and standard deviation for this
distribution?
b. What is the probability of exactly 17 successes?
c. What is the probability of fewer than 20 successes?
d. What is the probability of more than 12 successes?

1. Normal Approximation to Binomial Assume
n = 10, p = 0.1.
a. Use the Binomial Probability function to compute the P(X =
2)
b. Use the Normal Probability distribution to approximate the
P(X = 2)
c. Are the answers the same? If not, why?

Normal Approximation to Binomial
Assume n = 100, p = 0.4.
Use the Binomial Probability function to compute the P(X =
40)
Use the Normal Probability distribution to approximate the P(X
= 40)
Are the answers the same? If not, why?

The normal approximation of the binomial distribution is
appropriate when
np ≥ 5.
n(1 − p) ≥ 5.
np ≤ 5.
n(1 −
p) ≤ 5 and np ≤ 5.
np ≥ 5 and n(1 − p) ≥ 5.

Find the normal approximation for the binomial probability of
(don't use binomial probability) A) P(x=4) where n=13 and P=.5 B) P
(X<3) where n =13 and P=.5

The normal approximation of the binomial distribution is
appropriate when:
A. np 10
B. n(1–p) 10
C. np ≤ 10
D. np(1–p) ≤ 10
E. np 10 and n(1–p) 10

Suppose X follows the Binomial Distribution with n=1000 and
p=0.002. Use the Poisson approximation to determine the probability
that X is at least 2.

suppose 1000 coins are tossed. use the normal curve
approximation to the binomial di distribution to find the
probability of getting the following result. exactly 490 heads or
more

A die is tossed 120 times. Use the normal curve approximation to
the binomial distribution to find the probability of getting the
following result. More than 18 5 's

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