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slavikrds [6]
3 years ago
10

According to a survey, 40% of adults watch a particular television show. Six adults are selected at random. The binomial distrib

ution below shows the probability that k out of 6 adults watch the television show.
P(k = 0) = 0.0467
P(k = 1) = 0.1866
P(k = 2) = 0.3110
P(k = 3) = 0.2765
P(k = 4) = 0.1382
P(k = 5) = 0.0369

The distribution is
a) symmetric.
b) skewed.
c) both symmetric and skewed.

The sum of the probabilities is:
Mathematics
2 answers:
iren [92.7K]3 years ago
7 0

Answer:

The distribution is  

b) skewed.

The sum of the probabilities is:

1

Step-by-step explanation:

In a binomial distribution, p represents the probability of success. Success in the sense that the event of interest happens. In the model presented, the probability of success p is 0.4 since we are informed that 40% of adults watch a particular television show.

The next quantity of significance in a binomial model is the number of independent trials, n. In our case there are 6 independent trials since we are told that 6 adults were selected at random. If we let the random variable K denote the number of adults out of the 6 who watch the television show, then K is a binomial random variable with parameters;

n = 6 and p = 0.4

A binomial distribution is only symmetric when either p is 0.5 or n is large. In the presented scenario none of this conditions is met since p is 0.4 while n is just 6 which is relatively small. Thus we conclude that the distribution is not symmetric but rather skewed.

The sum of the probabilities is any discrete probability distribution such as the bernoulli, binomial, negative binomial, poisson, or the geometric distribution is always equal to 1. That's a rule of thumb.

Sladkaya [172]3 years ago
6 0

Answer:

The distribution is Skewed.

The Sum of the Probabilities in the distribution is 1

Step-by-step explanation:

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MAVERICK [17]

Answer:

1. leave the radical symbol and don't try to convert it to a decimal form

2. The approximated value differs from the exact solution and doesn't give a true equation.

3. Depending on the case, if she needs a mathematical answer, the exact value should be used, but for more practical applications, the rounded decimal form would be more usable.

Step-by-step explanation:

The step by step solution to the equation:

4x^3=756\\x^3=\frac{756}{4} =189\\x=\sqrt[3]{189} \\x=\sqrt[3]{3^3*7} \\x=3*\sqrt[3]{7}

1.- Exact solution means that if in the final step when solving for x the value of  x^3 is not a perfect cube, one needs to leave it indicated as a radical expression (with the radical symbol).

in our case, the cubic root of 189 is not a perfect cube. The factor form of 189 is: 3^3*7, so there is a perfect cube factor (3^3), but the other factor (7) is a prime number. Therefore 3 can get out of the root, while 7 stays inside.

2.- The equation was solved above, in exact form. Now to solve it giving a decimal approximation, we use a calculator to find the cubic root of 7, which is an irrational number with infinite number of decimals, the first of which we type here: \sqrt[3]{7} = 1.91293118...

Therefore, the decimal approximation to the solving for x would be:

x=3*\sqrt[3]{7}=3*1,91293118...=5.73879...=5.74

Where we rounded to two decimals as requested.

When we replace the exact answer in the original expression, we get a perfect equality:

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While if we use the approximate answer, we get:

4*x^3=756\\\\4*(5.74)^3=756\\\\4*189.119224=756\\756.476896=756

which is NOT a true equality.

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\LARGE{ \boxed{ \mathbb{ \color{purple}{SOLUTION:}}}}

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