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It was reported that 23% of U.S. adult cellphone owners called a friend for advice about a purchase while in a store. If a sample of 15 U.S adult cellphone owners is selected, what is the probability that 7 called a friend for advice about a purchase while in a store

Answers

Answer 1

Answer:

Answer:

$P(X=7)$

And using the probability mass function we got:

$P(X=7)=(15C7)(0.23)^7 (1-0.23)^(15-7)=0.0271$

Step-by-step explanation:

Let X the random variable of interest, on this case we now that:

$X \sim Binom(n=15, p=0.23)$

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:

$nCx=(n!)/((n-x)! x!)$

And we want to find the following probability:

$P(X=7)$

And using the probability mass function we got:

$P(X=7)=(15C7)(0.23)^7 (1-0.23)^(15-7)=0.0271$

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Answers

Answer:

Step-by-step explanation:

i not fully sure if this is right

Consider the expression 8 – 4 / 2. One student says the answer is 2 and another says it is 6. Which student is correct? Explain what went wrong with the student who made a mistake.

Answers

Answer:

It is 6. The student who got a two did not use order of operations.

Step-by-step explanation:

PEMDAS

You must do division before subtraction. 4/2 = 2.

8 - 2 = 6

The value of the solid's surface area is equal to the value of the solid's volume. find the value of x. 5*6*x

Answers

Given

a cuboid with length, width, height dimensions 5, 6, x

Find

the value of x that makes the numerical value of the total surface area equal to the numerical value of the volume

Solution

The volume is given by

... V = L·W·H = 5·6·x = 30x

The area is given by

... A = 2(L·W + H(L+W)) = 2(5·6 +x(5+6)) = 2(30 +11x) = 60 +22x

When these are equal, we have

... 30x = 60 +22x

... 8x = 60

... x = 7.5

The desired value of x is 7.5.

The time needed for all college students to complete a certain paper-and-pencil maze follows a normal distribution with a population mean of 30 seconds and a population standard deviation of 3 seconds. You wish to see if the mean time μ (where μ stands for population mean) is changed by vigorous exercise, so you have a group of nine college students exercise vigorously for 30 minutes and then complete the maze. It takes them an sample average of 31.2 seconds to complete the maze. Use this information to test the hypotheses:

H0: μ = 30,

Ha: ≠30

at the significance level of 0.01.

You conclude:

a) There is not enough evidence to support the claim.

b) There is enough evidence to support the claim.

Answers

Answer:

The correct option is a

Step-by-step explanation:

From the question we are told that

The population mean is $\mu = 30\ seconds$

The standard deviation is $\sigma = 3 \ seconds$

The sample size is n = 9

The null hypothesis is $H_o: \mu = 30$

The alternative hypothesis is $H_a : \mu \ne 30$

The level of significance is $\alpha = 0.01$

The sample mean is $\= x = 31.2$

Generally the test statistics is mathematically represented as

$z = ( \= x - \mu )/( (\sigma)/(√(n) ) )$

=> $z = ( 31.2 - 30)/( (3)/(√(9) ) )$

=> $z = 1.2$

From the z table the area under the normal curve to the right corresponding to 1.2 is

$P(Z > 1.2) = 0.11507$

Generally the p-value is mathematically represented as

$p-value = 2 * P(Z > 1.2)$

=> $p-value = 2 *0.11507$

=> $p-value = 0.230$

From the value obtained w can see that

$p-value > \alpha$ hence

The decision rule is

Fail to reject the null hypothesis

The conclusion is there is not enough evidence to support the claim

Final answer:

To test the hypotheses, use a one-sample t-test to compare the sample mean to the population mean. Calculate the t-value and compare it to the critical t-value at the significance level of 0.01. If the calculated t-value falls within the critical region, reject the null hypothesis. Otherwise, fail to reject the null hypothesis.

Explanation:

To test the hypotheses, we can use a one-sample t-test since we know the population standard deviation and the sample size is small. The null hypothesis (H0) is that the population mean (μ) is equal to 30 seconds, while the alternative hypothesis (Ha) is that the population mean is not equal to 30 seconds.

Using the given information, we can calculate the t-value by using the formula:

t = (sample mean - population mean) / (population standard deviation / sqrt(sample size))

Once we have the t-value, we can compare it to the critical t-value at the significance level of 0.01. If the calculated t-value falls within the critical region, we reject the null hypothesis. If not, we fail to reject the null hypothesis and conclude that there is not enough evidence to support the claim.