Question
In: Statistics and Probability
For a binomial probability distribution, n = 130 and p = 0.60. Let x be the...
For a binomial probability distribution, n = 130 and p = 0.60. Let x be the number of successes in 130 trials. a. Find the mean and standard deviation of this binomial distribution.
a. Find the mean and the standard deviation of this binomial distribution.
b. Find to 4 decimal places P(x ≤ 75) using the normal approximation. P(x ≤ 75) =
c. Find to 4 decimal places P(67 ≤ x ≤ 72) using the normal approximation. P(67 ≤ x ≤ 72) =
Solutions
orchestra answered 2 years agoRelated Solutions
Assume a binomial probability distribution has p = 0.60 and n = 300. (a) What are...
Assume a binomial probability distribution has
p = 0.60
and
n = 300.
(a)
What are the mean and standard deviation? (Round your answers to
two decimal places.)
mean standard deviation
(b)
Is this situation one in which binomial probabilities can be
approximated by the normal probability distribution? Explain.
No, because np ≥ 5 and n(1 − p) ≥ 5.
Yes, because n ≥ 30. Yes, because
np ≥ 5 and n(1 − p) ≥ 5. No, because
np <...
In the binomial probability distribution, let the number of trials be n = 4, and let...
In the binomial probability distribution, let the number of
trials be n = 4, and let the probability of success be
p = 0.3310. Use a calculator to compute the following.
(a) The probability of three successes. (Round your answer to
three decimal places.)
(b) The probability of four successes. (Round your answer to three
decimal places.)
(c) The probability of three or four successes. (Round your answer
to three decimal places.)
Binomial Distribution. Suppose that X has a binomial distribution with n = 50 and p =...
Binomial Distribution. Suppose that X has a binomial
distribution with n = 50 and p = 0.6. Use Minitab to simulate 40
values of X.
MTB > random 40 c1;
SUBC > binomial 50 0.6.
Note: To find P(X < k) for any k > 0, use ‘cdf’ command;
this works by typing:
MTB > cdf;
SUBC > binomial 50 0.6.
(a) What proportion of your values are less than 30? (b) What is
the exact probability that X will...
Let X have a binomial distribution with parameters n = 25 and p. Calculate each of...
Let X have a binomial distribution with parameters
n = 25
and p. Calculate each of the following probabilities
using the normal approximation (with the continuity correction) for
the cases
p = 0.5, 0.6, and 0.8
and compare to the exact binomial probabilities calculated
directly from the formula for
b(x; n, p).
(Round your answers to four decimal places.)
(a)
P(15 ≤ X ≤ 20)
p
P(15 ≤ X ≤ 20)
P(14.5 ≤ Normal ≤ 20.5)
0.5
1
2
0.6...
Let X have a binomial distribution with parameters n = 25 and p. Calculate each of...
Let X have a binomial distribution with parameters
n = 25
and p. Calculate each of the following probabilities
using the normal approximation (with the continuity correction) for
the cases
p = 0.5, 0.6, and 0.8
and compare to the exact binomial probabilities calculated
directly from the formula for
b(x; n, p).
(Round your answers to four decimal places.)
P(20 ≤ X)
p
P(20 ≤ X)
P(19.5 ≤ Normal)
0.5
0.6
0.8
Let X have a binomial distribution with parameters n = 25 and p. Calculate each of...
Let X have a binomial distribution with parameters
n = 25
and p. Calculate each of the following probabilities
using the normal approximation (with the continuity correction) for
the cases
p = 0.5, 0.6, and 0.8
and compare to the exact binomial probabilities calculated
directly from the formula for
b(x; n, p).
(Round your answers to four decimal places.)
(a)
P(15 ≤ X ≤ 20)
p
P(15 ≤ X ≤ 20)
P(14.5 ≤ Normal ≤ 20.5)
0.5
0.6
0.8
(B)P(X...
For the binomial distribution with n = 10 and p = 0.4, where p is probability...
For the binomial distribution with n = 10 and p = 0.4, where p
is probability of success. Let X be the number of successes.
(a) Find the probability of three or more successes.
(b) Find the µ, E(X), and σ 2 , V ar(X)
Let x be a random variable that possesses a binomial distribution with p=0.5 and n=9. Using...
Let x be a random variable that possesses a binomial
distribution with p=0.5 and n=9. Using the binomial formula or
tables, calculate the following probabilities. Also calculate the
mean and standard deviation of the distribution. Round solutions to
four decimal places, if necessary.
P(x≥3)=
P(x≤8)=
P(x=5)=
μ=
σ=
A binomial probability distribution has p = 0.25 and n = 81. A) What are the...
A binomial probability distribution has p = 0.25 and n = 81.
A) What are the mean and standard deviation?
B) Is this situation one in which binomial probabilities can be
approximated by the normal probability distribution? Explain.
C) What is the probability of exactly 28 successes?
D) What is the probability of 18 to 22 successes?
E)What is the probability of 24 or fewer successes?
Assume a binomial probability distribution has p = 0.70 and n = 300.
Assume a binomial probability distribution has p = 0.70 and n = 300. (a) What are the mean and standard deviation? (Round your answers to two decimal places.) mean Incorrect: Your answer is incorrect. standard deviation Incorrect: Your answer is incorrect. (b) Is this situation one in which binomial probabilities can be approximated by the normal probability distribution? Explain. Yes, because np ≥ 5 and n(1 − p) ≥ 5. Yes, because n ≥ 30. No, because np < 5...
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