Mathematics, 29.02.2020 01:17 sophiat17

Suppose 60% of American adults believe Martha Stewart is guilty of obstruction of justice and fraud related to insider trading. We will take a random sample of 100 American adults and ask them the question. Then the sampling distribution of the sample proportion of people who answer yes to the question is:a. neither Normal, not Binomial. b. approximately Normal, with unknown mean and standard deviation. c. approximately Normal, with mean 0.6 and standard error 0.04899.d. Binomial, with n=100 and p=0.60.

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Since the sample size is large enough (n>30) and the probability of success is near to 0.5, and we have that $n\hat p = 6010$ and $n(1-\hat p) = 4010$ we can assume that the distribution for $\hat p$ is normal

The population proportion have the following distribution

$\hat p \sim N(\hat p,\sqrt{\frac{\hat p(1-\hat p)}{n}})$

The mean is given by:

$\mu_p = 0.6$

$\sigma_p = \sqrt{\frac{0.6*(1-0.6)}{100}}=0.04899$

So then we can conclude that the best answer would be:

c. approximately Normal, with mean 0.6 and standard error 0.04899

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

represent the real population proportion of interest

$\hat p$ represent the estimated proportion for the sample

n is the sample size required (variable of interest)

Solution to the problem

The population proportion have the following distribution

$\hat p \sim N(\hat p,\sqrt{\frac{\hat p(1-\hat p)}{n}})$

The mean is given by:

$\mu_p = 0.6$

$\sigma_p = \sqrt{\frac{0.6*(1-0.6)}{100}}=0.04899$

So then we can conclude that the best answer would be:

c. approximately Normal, with mean 0.6 and standard error 0.04899

Answer from: Quest

step-by-step :

Answer from: Quest

see attached

step-by-step explanation:

given the function as;

$f(x)=2x^3-7x^2+2x+3$

write the equation replacing f(x) with y

$y=2x^3-7x^2+2x+3$

form and fill a table containing values of y with corresponding values of x

you can take a range for values of x as -3≤x≤3

solving for x=-3

$f(-3)=2*-3^3-7*-3^2+2*-3+3=2*-27-63+-6+3=-54-63-6+3y=-120$

for x=-2

$f(-2)=2*-2^3-7*-2^2+2*-2+3=2*-8-28+-4+3=-16-28-4+3=-45$

repeat the same procedure to get the values of y for the remaining ,x=-1 to x=3

plot the values of y against values of x and obtain the following graph

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