Solve the following inequality. -4x + 5 2 25 + 6x A. X2 B. XS2 C. XS-2 OD. XX-2

Suppose a random variable, x, arises from a binomial experiment. If n = 6, and p = 0.30, find the following probabilities using

AlladinOne [14]

Answer:

a) P(X=1) = 0.302526

b) P(X=5) = 0.010206

c) P(X=3) = 0.18522

d) P(X≤3) = 0.92953

e) P(X≥5) = 0.010935

f) P(X≤4) = 0.989065

Explanation:

Binomial experiments are modeled by the formula:

$P(X=x)=C(n,x)\cdot p^x\cdot (1-p)^{(n-x)}$

Where

P(X=x) is the probability of exactly x successes

$C(n,x)=\dfrac{n!}{x!\cdot (n-x)!}$

p is the probability of one success, which must be the same for every trial, and every trial must be independent of other trial.

n is the number of trials

1 - p is the probability of fail

there are only two possible outcomes for each trial: success or fail.

a.) P (x=1)

$P(X=1)=\dfrac{6!}{1!\cdot (6-1)!}\times (0.3)^1\times(1-0.3)^{(6-1)}=0.302526$

b.) P (x=5)

$P(X=5)=\dfrac{5!}{5!\cdot (6-5)!}\times (0.3)^5\times (1-0.3)^{(6-5)}=0.010206$

c.) P (x=3)

Using the same formula:

$P(X=3)=0.18522$

d.) P (x less than or equal to 3)

P(X≤3)= P(X=3) + P(X=2) + P(X=1) + P(X=0)

Also,

P(X≤3) = 1 - P(X≥4) = 1 - P(X=4) - P(X=5) - P(X=6)

You can use either of those approaches. The result is the same.

Using the second one:

P(X=4) = 0.059335
P(X=5) = 0.010206
P(X=6) = 0.000729

P(X≤3) = 1 - 0.05935 - 0.010206 - 0.000729 = 0.92953

e.) P(x greather than or equal to 5)

P(X≥5) = P(X=5) + P(X=6)

P(X≥5) = 0.010206 + 0.000729 = 0.010935

f.) P(x less than or equal 4)

P(X≤4) = 1 - P(X≥5) = 1 - P(X=5) - P(X=6)

P(X≤4) = 1 - 0.010206 - 0.000729 = 0.989065

5 0

3 years ago

the temperature at noon on a monday in december was -11°c. by noon on tuesday it has warmed by 17°c. what was the temperature at

Annette [7]

0centigrade anwser gotme

6 0

3 years ago

What is 41/12 as a mixed number

Mekhanik [1.2K]

The answer is 3 5/12

If you would like for me to show work. Let me know in a comment below and I will edit this.

Hope this helps you :)

4 0

3 years ago

Find a recursive formula for the sequence:

SVETLANKA909090 [29]

Answer:

$a_n=-2a_{n-1}+1$

Step-by-step explanation:

Successive terms do not have a common difference or ratio, so the sequence is not arithmetic or geometric. We can get a clue as to its nature a couple of places:

from the alternating signs, says there is a negative multiplier involved
from the answer choices

It is helpful to look at the differences of terms:

-5-3 = -8

11 -(-5) = 16

-21-11 = -32

These have a common ratio of -2, so match an exponential form with a ratio of -2 (the last answer choice). Trying that choice with n=1, 2, 3, 4 gives ...

a[1] = 3

a[2] = -2(3) +1 = -5

a[3] = -2(-5) +1 = 11

a[4] = -2(11) +1 = -21

These match the given sequence, so the appropriate recursive formula is ...

$\boxed{a_n=-2a_{n-1}+1}$