Question

Consider a binomial probability distribution with p=.35 and n=7.
what is the probability of the following?

a. exactly three successes P(x=3)

b. less than three successes P(x<3)

c. five or more successes P(x>=5)

Answer #1

Let X be a binomial random variable with p = 0.35 and n=7

X ~ Binomial ( n = 7, p = 0.35)

Using Excel we find following probabilities,

a) P(X = 3) = BINOMDIST(3, 7, 0.35, 0) = 0.26787094

=> P(X = 3) = **0.2679** (rounded to 4 decimal
places)

b)

P(X < 3)

= P(X <= 2)

= BINOMDIST(2, 7, 0.35, 1)

= 0.53228332

=> P(X < 3) = **0.5323** (rounded to 4
decimal places)

c)

P(X >= 5)

= 1 - P(X < 5)

= 1 - P(X <= 4)

= 1 - BINOMDIST(4, 7, 0.35, 1)

= 0.05560754

=> P(X >= 5) = **0.0556** (rounded to 4
decimal places)

Consider a binomial probability distribution with
pequals=0.35
and
nequals=7.
What is the probability of the following?
a)
exactly three successes
b)
less than three successes
c)
fivefive
or more successes

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?

For the binomial distribution with n = 10 and p = 0.3, find the
probability of: 1. Five or more successes. 2. At most two
successes. 3. At least one success. 4. At least 50% successes

Consider a binomial random variable with n = 7 and p = 0.8. Let
x be the number of successes in the sample. Evaluate the
probability. (Round your answer to three decimal places.) a. P(x
< 3) b. P(x = 3)

Consider a binomial probability distribution with
pequals=0.2
Complete parts a through c below.
a. Determine the probability of exactly
three
successes when
nequals=5
Upper P left parenthesis 3 right
parenthesisP(3)equals=nothing
(Round to four decimal places as needed.)b. Determine the
probability of exactly
three
successes when
nequals=6
Upper P left parenthesis 3 right
parenthesisP(3)equals=nothing
(Round to four decimal places as needed.)c. Determine the
probability of exactly
three
successes when
nequals=7
Upper P left parenthesis 3 right
parenthesisP(3)equals=nothing
(Round to four decimal...

Study the binomial distribution table. Notice that the
probability of success on a single trial p ranges from
0.01 to 0.95. Some binomial distribution tables stop at 0.50
because of the symmetry in the table. Let's look for that symmetry.
Consider the section of the table for which n = 5. Look at
the numbers in the columns headed by p = 0.30 and
p = 0.70. Do you detect any similarities? Consider the
following probabilities for a binomial experiment...

A
random variable follows a binomial distribution with a probability
of success equal to 0.52. For a sample size of n=7, find the values
below.
a. the probability of exactly 3 successes
b. the probability of 4 or more successes
c. the probability of exactly 7 successes
d. the expected value of the random variable

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

A random variable follows a binomial distribution with a
probability of success equal to 0.69 For a sample size of N=11,
find the values below.
a. the probability of exactly 3 successes
b. the probability of 7 or more successes
c. the probability of exactly 10 successes
d. the expected value of the random variable

Consider a binomial random variable with n = 8 and p = .7 Let be
the number of successes in the sample.
P(x<= 3)

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