8 hundreds, ___ ones, 3 thousands, 7 ones Fill in the blank Thanks if you answered

According to the Knot, 22% of couples meet online. Assume the sampling distribution of p follows a normal distribution and answe

Ann [662]

Using the normal distribution and the central limit theorem, we have that:

a) The sampling distribution is approximately normal, with mean 0.22 and standard error 0.0338.

b) There is a 0.1867 = 18.67% probability that in a random sample of 150 couples more than 25% met online.

c) There is a 0.2584 = 25.84% probability that in a random sample of 150 couples between 15% and 20% met online.

<h3>Normal Probability Distribution</h3>

In a normal distribution with mean $\mu$ and standard deviation $\sigma$ , the z-score of a measure X is given by:

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

It 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, which is the percentile of X.

By the Central Limit Theorem, for a proportion p in a sample of size n, the sampling distribution of sample proportion is approximately normal with mean $\mu = p$ and standard deviation $s = \sqrt{\frac{p(1 - p)}{n}}$ , as long as $np \geq 10$ and $n(1 - p) \geq 10$ .

In this problem:

22% of couples meet online, hence p = 0.22.

A sample of 150 couples is taken, hence n = 150.

Item a:

The mean and the standard error are given by:

$\mu = p = 0.22$

$s = \sqrt{\frac{p(1 - p)}{n}} = \sqrt{\frac{0.22(0.78)}{150}} = 0.0338$

The sampling distribution is approximately normal, with mean 0.22 and standard error 0.0338.

Item b:

The probability is one subtracted by the p-value of Z when X = 0.25, hence:

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

By the Central Limit Theorem:

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

$Z = \frac{0.25 - 0.22}{0.0338}$

Z = 0.89

Z = 0.89 has a p-value of 0.8133.

1 - 0.8133 = 0.1867.

There is a 0.1867 = 18.67% probability that in a random sample of 150 couples more than 25% met online.

Item c:

The probability is the p-value of Z when X = 0.2 subtracted by the p-value of Z when X = 0.15, hence:

X = 0.2:

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

$Z = \frac{0.2 - 0.22}{0.0338}$

Z = -0.59

Z = -0.59 has a p-value of 0.2776.

X = 0.15:

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

$Z = \frac{0.15 - 0.22}{0.0338}$

Z = -2.07

Z = -2.07 has a p-value of 0.0192.

0.2776 - 0.0192 = 0.2584.

There is a 0.2584 = 25.84% probability that in a random sample of 150 couples between 15% and 20% met online.

To learn more about the normal distribution and the central limit theorem, you can check brainly.com/question/24663213

4 0

2 years ago

What is the following product?

KiRa [710]

ANSWER

$2 \sqrt{42} +7 \sqrt{2}- 6- \sqrt{21}$

EXPLANATION

The given product is:

$( \sqrt{14} - \sqrt{3} )( \sqrt{12} + \sqrt{7} )$

We expand using the distributive property to obtain:

$\sqrt{14}( \sqrt{12} + \sqrt{7}) -\sqrt{3}( \sqrt{12} + \sqrt{7} )$

Extract the perfect squares to get:

$\sqrt{14}(2 \sqrt{3} + \sqrt{7}) -\sqrt{3}( 2\sqrt{3} + \sqrt{7} )$

Expand further to get;

$2 \sqrt{42} +7 \sqrt{2}- 2(3) - \sqrt{21}$

This simplifies to,

$2 \sqrt{42} +7 \sqrt{2}- 6- \sqrt{21}$

5 0

3 years ago

You have $55,000 in savings account that pays 2% intrest per year. The inflation rate that year is 3.24%. How much do you make i

Sever21 [200]

Your interest formula is given to you.

Interest in a year = principal (the amount invested) * rate (the interest rate) * period (the time you're measuring)

Interest = 55,000 * 2% * 1 year = 55,000 * 0.02 * 1 = $1,100

How much would you need to have made for your spending power to keep with inflation? Your interest rate would have needed to match the inflation rate, otherwise prices are going up faster than you're saving.

Required interest = 55,000 * 3.24% * 1 year = 55,000 * 0.0324 * 1 = $1,782

How much buying power did you lose? The difference between your required interest and your actual interest.
Buying power lost = 1,782 - 1,100 = $682. You lost this much in buying power.

Hope that helped :)

6 0

3 years ago

What is the y-intercept of the graph of y = 4^x-2?

mixas84 [53]

Answer: Hope this helps you.

-2

Step-by-step explanation:

y = mx+b (B is y-int)

y = 4^x-2

-2 is clearly replacing the b (y-int) meaning b, the y-int, is -2

5 0

2 years ago

Read 2 more answers

A right triangle has the hypotenuse c = 12 cm and an angle A = 30°. Find the length of side a, which is opposite angle A. A. 7.4

vagabundo [1.1K]

On the one hand we know that sin(30) = 1/2. On the other hand we know that sin(A) = a/c. From these two relations we obtain that 1/2 = a/c <=> 1/2 = a/12 <=> a = 12*1/2 <=> a = 6. So the answer is D. 6cm.

5 0

3 years ago