Mathematics, 23.03.2020 19:27 phancharamachasm

Suppose that you take a sample of 250 adults. If the population proportion of adults who watch news videos is 0.58, what is the probability that fewer than half in your sample will watch news videos

Answers: 2

Show answers

Answers

Answer from: kruzyoungblood8

0.36% probability that fewer than half in your sample will watch news videos

Step-by-step explanation:

To solve this question, i am going to use the binomial approximation to the normal.

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 = 250, p = 0.58

$\mu = E(X) = 250*0.58 = 145$

$\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{250*0.58*0.42} = 7.80$

If the population proportion of adults who watch news videos is 0.58, what is the probability that fewer than half in your sample will watch news videos

Half: 0.5*250 = 125

Less than half is 124 or less

So this is the pvalue of Z when X = 124

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

$Z = \frac{124 - 145}{7.8}$

Z = -2.69

Z = -2.69 has a pvalue of 0.0036

0.36% probability that fewer than half in your sample will watch news videos

Answer from: Quest

a. since the profit made in 2012 is equal to the profit made in 2014, the profit is symmetric about the line y = 120,000.

step-by-step explanation:

Answer from: Quest

step-by-step explanation:

73-22=51 the mass number minus the amount of protons gives you the amount of neutrons

Another question on Mathematics

Mathematics, 21.06.2019 13:00

Write a division equation you could use to find a, the number of miles ava is in charge of. what is the value of a? write your answer is simplist form

Answers: 1

Answer

Mathematics, 21.06.2019 17:00

Yosef can eat 21 jamuns while rose can eat just 15 . complete the blank. yosef can eat % more jamuns than rose.

Answers: 1

Answer

Mathematics, 21.06.2019 17:10

If angle 2=3x +1 and angle 3=2x +4what is angle 2

Answers: 1

Answer

Mathematics, 21.06.2019 18:00

Each month, a shopkeeper spends 5x + 14 dollars on rent and electricity. if he spends 3x−5 dollars on rent, how much does he spend on electricity? for which value(s) of x is the amount the shopkeeper spends on electricity less than $100? explain how you found the value(s).

Answers: 2

Answer

You know the right answer?

Suppose that you take a sample of 250 adults. If the population proportion of adults who watch news...

Questions