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?

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 and standard deviation , the zscore of a measure X is given by:

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 and standard deviation , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean and standard deviation .

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 and standard deviation

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

This means that

Sample of 400 Americans

This means that

Mean and standard deviation:

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

By the Central Limit Theorem

has a pvalue of 0.9995

X = 0.4

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

i dont know sorry

step-by-step explanation:

you are playing an adventure game on your computer. you come across a troll who won't let you pass and there is no other way to get to the other side of the river except over the bridge he is guarding.

the troll is a nerd. he takes great delight in watching people struggle with his problems. very few get them. he only gives you one chance and then he changes the puzzle. you have to solve this one.

before you are four blocks. they are numbered 11,6, -7,21.

he tells that the answer he wants is minus and between -1 and - 2. you can use +, -, ×, ÷   ( and ) as many times as you like or no times at all. you don't like the way he's looking at you, but you need to cross the bridge. what do you do?