12 out of 15 people in the US like to eat out. if 400 people selected eating out how many people took the survey?

A CBS News/New York Times survey found that 97% of Americans believe that texting while driving should be outlawed (CBS News web

Murrr4er [49]

Answer:

a) $P(X\geq 8)=0.0317+0.228+0.737=0.9972$

b) $P(X>95) =1-P(X$

Step-by-step explanation:

Previous concepts

A Bernoulli trial is "a random experiment with exactly two possible outcomes, "success" and "failure", in which the probability of success is the same every time the experiment is conducted". And this experiment is a particular case of the binomial experiment.

The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".

The probability mass function for the Binomial distribution is given as:

$P(X)=(nCx)(p)^x (1-p)^{n-x}$

Where (nCx) means combinatory and it's given by this formula:

$nCx=\frac{n!}{(n-x)! x!}$

The complement rule is a theorem that provides a connection between the probability of an event and the probability of the complement of the event. Lat A the event of interest and A' the complement. The rule is defined by: $P(A)+P(A') =1$

Part a

We want this probability:

$P(X\leq 12)$

$P(X\geq 8)=P(X=8)+P(X=9)+P(X=10)$

$P(X=8)=(10C8)(0.97)^8 (1-0.97)^{10-8}=0.03174$

$P(X=9)=(10C9)(0.97)^9 (1-0.97)^{10-9}=0.2287$

$P(X=10)=(10C10)(0.97)^{10} (1-0.97)^{10-10}=0.7374$

$P(X\geq 8)=0.0317+0.228+0.737=0.9972$

Part b

We need to check if we can use the normal approximation , the conditions are:

$np=100*0.97=97>10$ and $n(1-p)=100*(1-0.97)=3$

On this case the second condition is not satisfied, but the problem says that we can use it. So then if we apply the normal approximation to the binomial distribution in our case:

$X \sim N(\mu=97,\sigma=1.706)$

We can use the z score formula given by:

$z=\frac{x-\mu}{\sigma}$

And we want this probability:

$P(X>95) = P(Z>\frac{95-97}{1.706})= P(Z>-1.17)$

And we can use the complment rule and we got:

$P(X>95) =1-P(X$

6 0

3 years ago

If f(x) is differentiable for the closed interval [-4, 0] such that f(-4) = 5 and f(0) = 9, then there exists a value c, -4 <

WITCHER [35]

<span>Mean value theorem

For $f:[a,b] \rightarrow \mathbb{R}$ exist $c \in (a,b)$ such that

$f'(c)=\dfrac{f(b)-f(a)}{b-a}$

$f'(c)=\dfrac{f(-4)-f(0)}{-4-0}=\dfrac{5-9}{-4}=\dfrac{-4}{-4}=\boxed{1}$ </span>

3 0

3 years ago

(5x - 11)<br> (2x + 20)<br> (11x-63)

MrRa [10]

Ancbbbnm,..vbnm,.

Step-by-step explanation:

6 0

3 years ago

What is the solution to the inequality 6 - 2x < 4?

san4es73 [151]

Answer:

the answer is defintly going to be B sincr er csny trlly know whats going on with this planet

Step-by-step explanation:

3 0

3 years ago

An object moves from the position +16 m to the position +47 m in 12 s. What is its total displacement? What is its average veloc

Brrunno [24]

Given that an object moves from the position +16 m to the position +47 m in 12 s. Now we need to find about what is its total displacement and what is its average velocity.

We know that displacement is the object's overall change in position.

So total displacement is given by:

Displacement = (+47) - (+16) = +31

Now velocity is given by ratio of displacement and time so final answer for velocity will be :

$Velocity=\frac{displacement}{time}=\frac{+31}{12}=2.583333$

Which is approx 2.6 m/s.

5 0

3 years ago

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