Question

Suppose that *Y* has a binomial distribution with

* p* = 0.60.

(a)

Use technology and the normal approximation to the binomial distribution to compute the exact and approximate values of

* P*(

for *n* = 5, 10, 15, and 20. For each sample size, pay
attention to the shapes of the binomial histograms and to how close
the approximations are to the exact binomial probabilities. (Round
your answers to five decimal places.)

* n* = 5

exact value

* P*(

= approximate value

* P*(

≈

* n* = 10

exact value

* P*(

= approximate value

* P*(

≈

* n* = 15

exact value

* P*(

= approximate value

* P*(

≈

* n* = 20

exact value

* P*(

= approximate value

* P*(

≈

Answer #1

For each n,

the exact values are calculated in excel using the formula:

= BINOMDIST(np+1,n,p,TRUE) , where n, p and np are according to the values given.

the approximate values are calculated in excel using the formula:

=NORMDIST(np+1,np,npq,TRUE), where np and npq are selected in accordance.

p= | 0.6 | |||

n= | 5 | 10 | 15 | 20 |

np= | 3 | 6 | 9 | 12 |

npq= | 1.2 | 2.4 | 3.6 | 4.8 |

Exact value= | 0.92224 | 0.83271 | 0.782722 | 0.749989 |

Approximate value = | 0.797672 | 0.661539 | 0.609409 | 0.582516 |

Suppose X is binomial random variable with n = 18 and p = 0.5.
Since np ≥ 5 and n(1−p) ≥ 5, please use binomial distribution to
find the exact probabilities and their normal approximations. In
case you don’t remember the formula, for a binomial random variable
X ∼ Binomial(n, p), P(X = x) = n! x!(n−x)!p x (1 − p) n−x . (a) P(X
= 14). (b) P(X ≥ 1).

Suppose that x has a binomial distribution with n
= 202 and p = 0.47. (Round np and n(1-p) answers
to 2 decimal places. Round your answers to 4 decimal places. Round
z values to 2 decimal places. Round the intermediate value (σ) to 4
decimal places.)
(a) Show that the normal approximation to the
binomial can appropriately be used to calculate probabilities about
x
np
n(1 – p)
Both np and n(1 – p) (Click to select)≥≤
5
(b)...

Suppose that x has a binomial distribution with n = 199 and p =
0.47. (Round np and n(1-p) answers to 2 decimal places. Round your
answers to 4 decimal places. Round z values to 2 decimal places.
Round the intermediate value (σ) to 4 decimal places.) (a) Show
that the normal approximation to the binomial can appropriately be
used to calculate probabilities about x. np n(1 – p) Both np and
n(1 – p) (Click to select) 5 (b)...

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.

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)

Assume XX has a binomial distribution. Use the binomial formula,
tables, or technology to calculate the probability of the indicated
event:
a. n=20, p=0.7n=20, p=0.7
P(13 ≤ X ≤ 16)=P(13 ≤ X ≤ 16)=
Round to four decimal places if necessary
b. n=17, p=0.2n=17, p=0.2
P(2 < X < 5)=P(2 < X < 5)=
Round to four decimal places if necessary
please provide correct answer.

Compute P(x) using the binomial probability formula. Then
determine whether the normal distribution can be used to estimate
this probability. If so, approximate P(x) using the normal
distribution and compare the result with the exact probability.
n=73 p=0.82 x=53
a) Find P(x) using the binomial probability distribution:
P(x) =
b) Approximate P(x) using the normal distribution:
P(x) =
c) Compare the normal approximation with the exact
probability.
The exact probability is less than the approximated probability
by _______?

1. Normal Approximation to Binomial Assume
n = 10, p = 0.1.
a. Use the Binomial Probability function to compute the P(X =
2)
b. Use the Normal Probability distribution to approximate the
P(X = 2)
c. Are the answers the same? If not, why?

Compute P(X) using the binomial probability formula. Then
determine whether the normal distribution can be used to estimate
this probability. If so, approximate P(X) using the normal
distribution and compare the result with the exact probability.
n=50, p=0.50, and x=17 For n=50, p=0.5, and X=17, use the
binomial probability formula to find P(X).
Q: By how much do the exact and approximated probabilities
differ?
A. ____(Round to four decimal places as needed.)
B. The normal distribution cannot be used.

Suppose X has a binomial distribution with p = 0.3 and n = 20.
Note that E[X] = 6. Compute P(5 <X < 8) exactly and
approximately with the CLT. Answers: 0.4851 from normal, 0.4703
from exact computation.
please write the process

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