Question

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.

Answer #1

TOPIC:Binomial distribution.

Let X be a binomial random variable with p = 0.7
a) For n = 3, find P(X=1)
b) For n = 5, find P(X≤3)

Let X be a binomial random variable with n =
8, p = 0.4. Find the following values. (Round your answers
to three decimal places.)
(a)
P(X = 4)
(b)
P(X ≤ 1)
(c)
P(X > 1)

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.

Suppose that X is a binomial random variable with n=5 and
p=1/4.
Let ? = (? − 3) 2 .
1. What is the space of Y?
2. What is the mean of Y?
3. What is the probability that Y<2? (Round to 4 decimal
places.)
4. What is the probability that Y=1? (Round to 4 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
need step and sloution

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)

Let X represent a binomial random variable with
n = 360 and p = 0.82. Find the following
probabilities. (Do not round intermediate calculations.
Round your final answers to 4 decimal places.
Probability
a.
P(X ≤ 290)
b.
P(X > 300)
c.
P(295 ≤ X ≤ 305)
d.
P(X = 280)

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).

Let X represent a binomial random variable with n = 170 and p =
0.6. Find the following probabilities. (Do not round intermediate
calculations. Round your final answers to 4 decimal places.)
Probability
a.P(X ≤ 100)
b.P(X > 110)
c.P(105 ≤ X ≤ 115)
d.P(X = 90)

Let X be a binomial random variable with n =
400 trials and probability of success p = 0.01. Then the
probability distribution of X can be approximated by
Select one:
a. a Hypergeometric distribution with N =
8000, n = 400, M = 4.
b. a Poisson distribution with mean 4.
c. an exponential distribution with mean 4.
d. another binomial distribution with n =
800, p = 0.02
e.
a normal distribution with men 40 and variance 3.96.

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