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Murrr4er [49]
2 years ago
12

(a)

Mathematics
1 answer:
mariarad [96]2 years ago
3 0

Answer:

x + 4x = 90

x = 90/5 = 18°

Step-by-step explanation:

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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 <em>normal distribution and the central limit theorem</em>, 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 <u>one subtracted by the p-value of Z when X = 0.25</u>, 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 <u>p-value of Z when X = 0.2 subtracted by the p-value of Z when X = 0.15</u>, 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 <em>normal distribution and the central limit theorem</em>, you can check brainly.com/question/24663213

4 0
2 years ago
A school ends the year with 651 students. This is a 5% increase from the start of the school year.
Jet001 [13]
ANSWER:

n = 1.05n divided by 105 times 100

OR

n = (the number of students at the END of the school year) divided by 105 times 100

WORKING OUT:

1.05n = 651 students
1n = 651/105 times 100 = ANSWER
5 0
3 years ago
Read 2 more answers
Lia has a red ribbon that is 2 1/12 inches long she has a blue ribbon that is 4 time as many inches as long how many inches long
Rom4ik [11]

Answer:

8 1/3 inches

Step-by-step explanation:

Length of the ribbon = 2 1/12 inches

Blue ribbon is 4 time as many inches as long as red

Length of the blue ribbon = 4 * 2 1/12

Length of the blue ribbon = 4 * 25/12

Length of the blue ribbon = 100/12

Length of the blue ribbon= 25/3

Length of the blue ribbon = 8 1/3 inches

Hence the blue ribbon is 8 1/3 inches long

6 0
3 years ago
A backpack costs $18 and has a 7 percent tax. How much will Sheila have to pay for the backpack after tax?
Dmitry_Shevchenko [17]

Answer:

19.26

Step-by-step explanation:

7% of 18 is 1.26

1.26+18=19.26

4 0
3 years ago
*Awarding Brainliest!*
Alex73 [517]

Answer:

Step-by-step explanation:

The angles labeled 4y - 8 and 79 + y are called vertical angles, and definition, vertical angles are congruent.  That means algebraically, that

4y - 8 = 79 + y and

3y = 87 and

y = 29

8 0
3 years ago
Read 2 more answers
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