Question

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.

Answer #1

Given : n = 100 p = 0.20 therefore , q = 1 - p = 0.80

Also ,

Since , np = 100*0.20 = 20 > 10 and nq = 100*0.80 = 80 > 10

Therefore , by using the normal approximation to the binomial distribution ,

We want to find the P(X > 18)

Therefore , = n * p = 100*0.20 = 20

= n * p * q = 100 * 0.20 * 0.80 = 4

Therefore ,

P(X > 18) = 1 - P(X > 18) = 1 - P((x - ) / < (18- 20) / 4) = 1 - P(Z < -0.5) = 1-0.3085 = 0.6915

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

Suppose Y is a random variable that follows a binomial
distribution with n = 25 and π = 0.4. (a) Compute the exact
binomial probability P(8 < Y < 14) and the normal
approximation to this probability without using a continuity
correction. Comment on the accuracy of this approximation. (b)
Apply a continuity correction to the approximation in part (a).
Comment on whether this seemed to improve the approximation.

X is a binomial random variable with n = 15 and p = 0.4.
a. Find using the binomial distribution.
b. Find using the normal approximation to the binomial
distribution.

Let X be a binomial random variable with n =
100 and p = 0.2. Find approximations to these
probabilities. (Round your answers to four decimal places.)
(c) P(18 < X < 30)
(d) P(X ≤ 30)

True or False?
19. In a binomial distribution the random variable X is
discrete.
20. The standard deviation and mean are the same for the
standard normal distribution.
21. In a statistical study, the random variable X = 1, if the
house is colonial and X = 0 if the house is not colonial, then it
can be stated that the random variable is continuous. 22. For a
continuous distribution, P(X ≤ 10) is the same as P(X<10).
23. For...

Let
X be a binomial random variable with parameters n = 500 and p =
0.12. Use normal approximation to the binomial distribution to
compute the probability P (50 < X ≤ 65).

Suppose that x has a binomial distribution with
n = 200 and p = .4.
1. Show that the normal approximation to the binomial can
appropriately be used to calculate probabilities for
Make continuity corrections for each of the
following, and then use the normal approximation to the binomial to
find each probability:
P(x = 80)
P(x ≤ 95)
P(x < 65)
P(x ≥ 100)
P(x > 100)

1) Let X be a binomial random variable with p = 0.55, and n= 40.
Find the probability
that X is more than 2 standard deviations from the mean of X.

Let
x be binomial random variable with n=50 and p=.3. The probability
of less than or equal to 13 successes, when using the normal
approximation for binomial is ________. (Please show how to work
the problem).
a) -.6172
b) .3086
c) 3.240
d) .2324
e) .2676
f) -.23224

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.)

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