Mathematics, 10.03.2021 21:50, jermarae

37% of Americans say that math is the most important subject in school. In a random sample of 400 Americans, what is the probability that between 40% and 45% will say that math is the most important subject?

Answers: 3

Show answers

Answers

answered: maukjackie1974

0.1070 = 10.70% probability that between 40% and 45% will say that math is the most important subject

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution:

Problems of normal distributions 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.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean $\mu = p$ and standard deviation $s = \sqrt{\frac{p(1-p)}{n}}$

37% of Americans say that math is the most important subject in school.

This means that p = 0.37

Sample of 400 Americans

This means that n = 400

Mean and standard deviation:

$\mu = p = 0.37$

$s = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.37*0.63}{400}} = 0.0241$

What is the probability that between 40% and 45% will say that math is the most important subject?

This is the pvalue of Z when X = 0.45 subtracted by the pvalue of Z when X = 0.4. So

X = 0.45

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

By the Central Limit Theorem

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

$Z = \frac{0.45 - 0.37}{0.0241}$

Z = 3.31

Z = 3.31 has a pvalue of 0.9995

X = 0.4

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

$Z = \frac{0.4 - 0.37}{0.0241}$

Z = 1.24

Z = 1.24 has a pvalue of 0.8925

0.9995 - 0.8925 = 0.1070

0.1070 = 10.70% probability that between 40% and 45% will say that math is the most important subject

answered: Guest

30 units^2

step-by-step explanation:

area is l × w

the length is 3

and the width is 10

3 × 10= 30 units squared

What is the area of this rectangle? 13 units 23 units 26 units 30 units?

answered: Guest

is only a line? i think so

Other questions on the subject: Mathematics

Mathematics, 21.06.2019 19:30, woodfordmaliky

Louis wants to carpet the rectangular floor of his basement. the basement has an area of 864 square feet. the width of the basement is 2/3 it's length. what is the length of louis's basement

Answers: 1

continue

Mathematics, 21.06.2019 20:30, natebarr17

The interior angles formed by the side of a hexagon have measures of them up to 720° what is the measure of angle a

Answers: 2

continue

Mathematics, 21.06.2019 22:30, sonaihriley

Abucket of paint has spilled on a tile floor. the paint flow can be expressed with the function p(t) = 6(t), where t represents time in minutes and p represents how far the paint is spreading. the flowing paint is creating a circular pattern on the tile. the area of the pattern can be expressed as a(p) = 3.14(p)^2 part a: find the area of the circle of spilled paint as a function of time, or a[p(t)]. show your work. part b: how large is the area of spilled paint after 8 minutes? you may use 3.14 to approximate pi in this problem.

Answers: 2

continue

Mathematics, 22.06.2019 05:10, cocomorillo35181

What is the value of g(8) for the function g(x) in part c? what does this value mean in the context of the situation you described in part c?

Answers: 1

continue

Do you know the correct answer?

37% of Americans say that math is the most important subject in school. In a random sample of 400 Am...