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Triss [41]
3 years ago
8

A poll agency reports that 27 % of teenagers aged 12-17 own smartphones. A random sample of 85 teenagers is drawn. Round your an

swers to at least four decimal places as needed.
Mathematics
1 answer:
Paladinen [302]3 years ago
6 0

Answer:

Mean = цр = 0.27

Step-by-step explanation:

Note: The full question is attached as picture below

Given that,  p = 27 = 0.27  and n = 85

цр = P

Mean = цр = 0.27

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The amount of coffee that a filling machine puts into an 8-ounce jar is normally distributed with a mean of 8.2 ounces and a sta
nordsb [41]

Answer:

73.30% probability that the sampling error made in estimating the mean amount of coffee for all 8-ounce jars by the mean of a random sample of 100 jars will be at most 0.02 ounce

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 normally distributed samples are 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.

In this problem, we have that:

\mu = 8.2, \sigma = 0.18, n = 100, s = \frac{0.18}{\sqrt{100}} = 0.018

What is the probability that the sampling error made in estimating the mean amount of coffee for all 8-ounce jars by the mean of a random sample of 100 jars will be at most 0.02 ounce?

This is the pvalue of Z when X = 8.2 + 0.02 = 8.22 subtracted by the pvalue of Z when X = 8.2 - 0.02 = 8.18. So

X = 8.22

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

By the Central Limit Theorem

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

Z = \frac{8.22 - 8.2}{0.018}

Z = 1.11

Z = 1.11 has a pvalue of 0.8665

X = 8.18

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

Z = \frac{8.18 - 8.2}{0.018}

Z = -1.11

Z = -1.11 has a pvalue of 0.1335

0.8665 - 0.1335 = 0.7330

73.30% probability that the sampling error made in estimating the mean amount of coffee for all 8-ounce jars by the mean of a random sample of 100 jars will be at most 0.02 ounce

8 0
3 years ago
Do the political leanings of a network affect the news they report? During the the 2018-2019 Government shutdown, a left-leaning
daser333 [38]

Answer:

504

Step-by-step explanation:

We are solving for the left leaning poll

Total voters = 900 + 1100

= 2000

Number of voters who say trump was responsible = 56percent x 2000

= 1120

Number of those who say otherwise = 44% x 2000

= 880

For this network

Those who say trump is responsible = 1120 x900/2000

= 1008000/2000

= 504 registered voters

6 0
3 years ago
Use the box method to distribute and simplify (5x – 6)(x^2 – x– 3). Drag and
mina [271]

Answer:

The result will be: 5x³ -11x² -9x + 18

7 0
2 years ago
A cell phone company offers two plans to its subscribers. At the time new subscribers sign up, they are asked to provide some de
slavikrds [6]

Answer:HI

Step-by-step explanation:HI

3 0
2 years ago
NEED HELP ASAP<br><br><br> Find f(-2) for f(x) = 2(4)^x
viktelen [127]

Answer:

A.) \frac{1}{8}

Step-by-step explanation:

f(-2) means plug in -2 in for x for the equation f(x), therefore,

f(-2) = 2(4)^x = 2(4)^{-2} = \frac{1}{8}

4 0
2 years ago
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