Question

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.)

Answer #1

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

Suppose we have a binomial distribution with n trials
and probability of success p. The random variable
r is the number of successes in the n trials, and
the random variable representing the proportion of successes is
p̂ = r/n.
(a) n = 44; p = 0.53; Compute P(0.30
≤ p̂ ≤ 0.45). (Round your answer to four decimal
places.)
(b) n = 36; p = 0.29; Compute the probability
that p̂ will exceed 0.35. (Round your answer to four...

Given a random sample of size of
n equals =3,600
from a binomial probability distribution with
P equals=0.50,
complete parts (a) through (e) below.
Click the icon to view the standard normal table of the
cumulative distribution function
.a. Find the probability that the number of successes is greater
than 1,870.
P(X greater than>1 comma 1,870)
(Round to four decimal places as needed.)b. Find the
probability that the number of successes is fewer than
1 comma 1,765.
P(X less than<1...

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?

In the binomial probability distribution, let the number of
trials be n = 3, and let the probability of success be p = 0.3742.
Use a calculator to compute the following.
(a) The probability of two successes. (Round your answer to
three decimal places.)
(b) The probability of three successes. (Round your answer to
three decimal places.)
(c) The probability of two or three successes. (Round your
answer to three decimal places.)

If x is a binomial random variable where n = 100 and p = 0.20,
find the probability that x is more than 18 using the normal
approximation to the binomial. Check the condition for continuity
correction.

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?

Suppose that x has a binomial distribution with n
= 202 and p = 0.47. (Round np and n(1-p) answers
to 2 decimal places. Round your answers to 4 decimal places. Round
z values to 2 decimal places. Round the intermediate value (σ) to 4
decimal places.)
(a) Show that the normal approximation to the
binomial can appropriately be used to calculate probabilities about
x
np
n(1 – p)
Both np and n(1 – p) (Click to select)≥≤
5
(b)...

Suppose that x has a binomial distribution with n = 199 and p =
0.47. (Round np and n(1-p) answers to 2 decimal places. Round your
answers to 4 decimal places. Round z values to 2 decimal places.
Round the intermediate value (σ) to 4 decimal places.) (a) Show
that the normal approximation to the binomial can appropriately be
used to calculate probabilities about x. np n(1 – p) Both np and
n(1 – p) (Click to select) 5 (b)...

If x is a binomial random variable where n = 100 and p = 0.20,
find the probability that x is more than 18 using the normal
approximation to the binomial. Check the condition for continuity
correction
need step and sloution

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