1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
nevsk [136]
3 years ago
8

An IAB study on the state of original digital video showed that original digital video is becoming increasingly popular. Origina

l digital video is defined as professionally produced video intended only for ad-supported online distribution and viewing. According to IAB data, 30% of American adults 18 or older watch original digital videos each month.
1. Suppose that you take a sample of 100 U.S. adults, what is the probability that fewer than 25 in your sample will watch original digital videos?
Mathematics
1 answer:
never [62]3 years ago
5 0

Answer:

11.51% probability that fewer than 25 in your sample will watch original digital videos

Step-by-step explanation:

I am going to use the normal approximation to the binomial to solve this question.

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

The expected value of the binomial distribution is:

E(X) = np

The standard deviation of the binomial distribution is:

\sqrt{V(X)} = \sqrt{np(1-p)}

Normal probability distribution

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the zscore of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

When we are approximating a binomial distribution to a normal one, we have that \mu = E(X), \sigma = \sqrt{V(X)}.

In this problem, we have that:

n = 100, p = 0.30

So

\mu = E(X) = np = 100*0.3 = 30

\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{100*0.3*0.7} = 4.58

What is the probability that fewer than 25 in your sample will watch original digital videos?

Using continuity correction, this is P(X < 25 - 0.5) = P(X < 24.5), which is the pvalue of Z when X = 24.5. So

Z = \frac{X - \mu}{\sigma}

Z = \frac{24.5 - 30}{4.58}

Z = -1.2

Z = -1.2 has a pvalue of 0.1151

11.51% probability that fewer than 25 in your sample will watch original digital videos

You might be interested in
the cheerleading squad made 4 5/8 gallon of lemonade to sell at the basketball game. they sold 2 7/8 gallons. how many gallons w
andrezito [222]
4 5/8 = 37/8
2 7/8= 23/8
37/8-23/8=14/8=1 6/8=1 3/4
5 0
3 years ago
56+34=n+30? Do you add 56+34 =90-30=60 n=60?
slamgirl [31]

You're on the right track. Start by combining like terms on the left side of the equation by adding 56 and 34.

90 = n + 30, now subtract 30 from both sides of the equation to isolate the variable n.

60 = n is the answer.

4 0
3 years ago
Read 2 more answers
Identify the slope and the y-intercept of the line.<br> y = 3x + 9
Sonja [21]

Answer:

slope = -3 , y-intercept = 9

Step-by-step explanation:

6 0
2 years ago
Describe the transformation from the graph of f(x)=x+8 to the graph of g(x)=x-3
andreev551 [17]

Answer:

A.)

Step-by-step explanation:

Translations are as follows: Up is + on Y axis, down is - on Y axis. Right is + on X axis and left is - on X axis.

The function f(x) = x+8 is translated to (0,8) since their is no number in a bracket with x (example: f(x)= (x-2)+5 would be (2,5) since the X axis is taken as the opposite sign).

g(x) = x-3 translates to (0,-3) which is 11 units down from f(x)

7 0
3 years ago
One person can do a certain job in fifteen minutes, and another person can do the same job in ten minutes. How many minutes will
8_murik_8 [283]
It would take 5 because they could do it twice as fast
8 0
3 years ago
Read 2 more answers
Other questions:
  • The sum of 86, 68, and 38 is 192. What else do you know about the sum of 68, 38, and 86?
    9·1 answer
  • solve each problem.simplify your answer.One inch on a map equals 375 miles.what do 5 3/4 inches represent.
    8·1 answer
  • How many times can 95 go into 96
    12·1 answer
  • For each of the following sequences, • Give a formula for the nth term in the sequence, • Give a recursive definition for the se
    15·1 answer
  • Y=6x +1<br> Function rule
    9·1 answer
  • Miss Parker invested a certain amount of money at 9.2% interest and another amount, $700 more than the first, at 10.4%. If the t
    5·1 answer
  • What is the net force on an object that has a 25N force pulling it to the right, and two 10N forces pulling it to the left?
    8·2 answers
  • -3xy-x²y²+1 is evaluated when x=-1 and y=-1 , then what is the exact value ?<br>​
    5·2 answers
  • What type of angle pairs are angles a and b?​
    6·2 answers
  • Evaluate 4+(7-5) <br><br>please help,y'all lol ​
    9·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!