Let X represent a binomial random variable with n = 360 and p = 0.82. Find the following probabilities.
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)
0.0063
Solutions
Expert Solution
a) P(X≤290)=0.2568 (Rounded final answer to 4 decimal
places)
Let X represent a binomial random variable with
n = 110 and p = 0.19. Find the following
probabilities. (Do not round intermediate calculations.
Round your final answers to 4 decimal places.)
a.
P(X ≤ 20)
b.
P(X = 10)
c.
P(X > 30)
d.
P(X ≥ 25)
Let X represent a binomial random variable with n = 180 and p =
0.23. Find the following probabilities. (Do not round intermediate
calculations. Round your final answers to 4 decimal places.)
a. P(X less than or equal to 45)
b. P(X=35)
c. P(X>55)
d. P (X greater than or equal to 50)
Let X represent a binomial random variable with n = 380 and p =
0.78. Find the following probabilities. (Round your final answers
to 4 decimal places.) Probability a. P(X ≤ 300) b. P(X > 320) c.
P(305 ≤ X ≤ 325) d. P( X = 290)
Let X be a binomial random variable with n =
11 and p = 0.3. Find the following values. (Round your
answers to three decimal places.)
(a)
P(X = 5)
(b)
P(X ≥ 5)
(c)
P(X > 5)
(d)
P(X ≤ 5)
(e)
μ = np
μ =
(f) σ =
npq
σ =
1.
(Use Computer) Let X represent a binomial random
variable with n = 400 and p = 0.8. Find the
following probabilities. (Round your final answers to 4
decimal places.)
Probability
a. P(X ≤ 330)
b. P(X > 340)
c. P(335 ≤ X ≤ 345)
d. P(X = 300)
2.
(Use computer) Suppose 38% of recent college graduates plan on
pursuing a graduate degree. Twenty three recent college graduates
are randomly selected.
a.
What is the...
(a) Let X be a binomial random variable with parameters (n, p).
Let Y be a binomial random variable with parameters (m, p).
What is the pdf of the random variable Z=X+Y?
(b) Let X and Y be indpenednet random variables. Let Z=X+Y.
What is the moment generating function for Z in terms of those
for X and Y?
Confirm your answer to the previous problem (a) via moment
generating functions.
Let X be a binomial random variable with parameters n = 5 and p
= 0.6.
a) What is P(X ≥ 1)?
b) What is the mean of X?
c) What is the standard deviation of X? (Show work)
If x is a binomial random variable, use the binomial
probability table to find the probabilities below.
a. P(x<6) for n = 15, p=0.2
b. P(x>=14) for n=20, p=0.8
c. P(x=23) for n=25, p=0.1
If x is a binomial random variable, use the binomial
probability table to find the probabilities below.
a. P(x=3) for n=10, p=0.5
b. P(x≤4) for n=15, p=0.3
c. P(x>1) for n=5, p=0.2
d. P(x<6) for n=15, p=0.8
e. P(x≥14) for n=25, p=0.8
f. P(x=3) for n=20, p=0.1