How does the model show 15-6? Choose the numbers that make the number sentences .circle numbers in the boxes.

An article written for a magazine claims that 78% of the magazine's subscribers report eating healthily the previous day. Suppos

Schach [20]

Answer:

89.44% probability that less than 80% of the sample would report eating healthily the previous day

Step-by-step explanation:

We use the binomial approximation to the normal to solve this question.

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:

$p = 0.78, n = 675$

So

$\mu = E(X) = np = 675*0.78 = 526.5$

$\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{675*0.78*0.22} = 10.76$

What is the approximate probability that less than 80% of the sample would report eating healthily the previous day?

This is the pvalue of Z when $X = 0.8*675 = 540$ . So

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

$Z = \frac{540 - 526.5}{10.76}$

$Z = 1.25$

$Z = 1.25$ has a pvalue of 0.8944

89.44% probability that less than 80% of the sample would report eating healthily the previous day

8 0

3 years ago

Suppose you have 3 pieces of string measuring 6 inches, 9 inches, and 12 inches. How many unique triangles can you form with the

siniylev [52]

A triangle should have 3 points and 3 sides. Let say that the point is ABC. Then the sides would be AB, AC and BC.
There are 3 strings with a different length that can be put into the sides. Assuming the string can be used once, then the possible way would be:
3!/(1+3-3)!= 3!/1!= 3*2*1= 6 ways

8 0

2 years ago

Two numbers whose sum is 44 and whose product is a maximum

Mashcka [7]

Answer:

x = y = 22

Step-by-step explanation:

It would help to know your math course. Do you know any calculus? I'll assume not.

Equations

x + y = 44

Max = xy

Solution

y = 44 - x

Max = x (44 - x) Remove the brackets

Max = 44x - x^2 Use the distributive property to take out - 1 on the right.

Max = - (x^2 - 44x ) Complete the square inside the brackets.

Max = - (x^2 - 44x + (44/2)^2 ) + (44 / 2)^2 . You have to understand this step. What you have done is taken 1/2 the x term and squared it. You are trying to complete the square. You must compensate by adding that amount on the end of the equation. You add because of that minus sign outside the brackets. The number inside will be minus when the brackets are removed.

Max = -(x - 22)^2 + 484

The maximum occurs when x = 22. That's because - (x - 22) becomes 0.

If it is not zero it will be minus and that will subtract from 484

x + y = 44

xy = 484

When you solve this, you find that x = y = 22 If you need more detail, let me know.

4 0

2 years ago

Find the length of each arc<br> r=13 ft x=90 degrees

VladimirAG [237]

Answer:

$13\pi/2$