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Aliun [14]
3 years ago
6

Suppose that a market research firm is hired to estimate the percent of adults living in a large city who have cell phones. 500

randomly selected adult residents in this city are surveyed to determine whether they have cell phones. Of the 500 people surveyed, 421 responded yes – they own cell phones. Using a 95% confidence level, compute a confidence interval estimate for the true proportion of adults residents of this city who have cell phones.
Mathematics
1 answer:
Alborosie3 years ago
6 0

Answer:

The 95% confidence interval estimate for the true proportion of adults residents of this city who have cell phones is (0.81, 0.874).

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of \pi, and a confidence level of 1-\alpha, we have the following confidence interval of proportions.

\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}

In which

z is the zscore that has a pvalue of 1 - \frac{\alpha}{2}.

For this problem, we have that:

n = 500, \pi = \frac{421}{500} = 0.842

95% confidence level

So \alpha = 0.05, z is the value of Z that has a pvalue of 1 - \frac{0.05}{2} = 0.975, so Z = 1.96.

The lower limit of this interval is:

\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.842 - 1.96\sqrt{\frac{0.842*0.158}{500}} = 0.81

The upper limit of this interval is:

\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.842 + 1.96\sqrt{\frac{0.842*0.158}{500}} = 0.874

The 95% confidence interval estimate for the true proportion of adults residents of this city who have cell phones is (0.81, 0.874).

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at the movies, la quinta paid for drinks and popcorn for herself and her two children. she spend twice as much on popcorn as on
jarptica [38.1K]

Answer:

Step-by-step explanation:

let the amount spent on popcorn be x and amount spent on drinks be y

If the total bill paid is  $17.94, then x+y =  $17.94

If she spend twice as much on popcorn as on drinks, then y = 2x

Substitute y = 2x into the original equation

x+y =  $17.94

x + 2x =  $17.94

3x =  $17.94

x =  $17.94/3

x = $5.98

Since y = 2x

y = 2($5.98)

y = $11.96

Therefore she spent  $5.98 on popcorn and $11.96 on drinks

4 0
3 years ago
Suppose that the national average for the math portion of the College Board's SAT is 515. The College Board periodically rescale
nasty-shy [4]

Answer:

a) 16% of students have an SAT math score greater than 615.

b) 2.5% of students have an SAT math score greater than 715.

c) 34% of students have an SAT math score between 415 and 515.

d) Z = 1.05

e) Z = -1.10

Step-by-step explanation:

To solve this question, we have to understand the normal probability distribution and the empirical rule.

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.

Empirical rule

The Empirical Rule states that, for a normally distributed random variable:

68% of the measures are within 1 standard deviation of the mean.

95% of the measures are within 2 standard deviation of the mean.

99.7% of the measures are within 3 standard deviations of the mean.

In this problem, we have that:

\mu = 515, \sigma = 100

(a) What percentage of students have an SAT math score greater than 615?

615 is one standard deviation above the mean.

68% of the measures are within 1 standard deviation of the mean. The other 32% are more than 1 standard deviation from the mean. The normal probability distribution is symmetric. So of those 32%, 16% are more than 1 standard deviation above the mean and 16% more then 1 standard deviation below the mean.

So, 16% of students have an SAT math score greater than 615.

(b) What percentage of students have an SAT math score greater than 715?

715 is two standard deviations above the mean.

95% of the measures are within 2 standard deviations of the mean. The other 5% are more than 2 standard deviations from the mean. The normal probability distribution is symmetric. So of those 5%, 2.5% are more than 2 standard deviations above the mean and 2.5% more then 2 standard deviations below the mean.

So, 2.5% of students have an SAT math score greater than 715.

(c) What percentage of students have an SAT math score between 415 and 515?

415 is one standard deviation below the mean.

515 is the mean

68% of the measures are within 1 standard deviation of the mean. The normal probability distribution is symmetric, which means that of these 68%, 34% are within 1 standard deviation below the mean and the mean, and 34% are within the mean and 1 standard deviation above the mean.

So, 34% of students have an SAT math score between 415 and 515.

(d) What is the z-score for student with an SAT math score of 620?

We have that:

\mu = 515, \sigma = 100

This is Z when X = 620. So

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

Z = \frac{620 - 515}{100}

Z = 1.05

(e) What is the z-score for a student with an SAT math score of 405?

We have that:

\mu = 515, \sigma = 100

This is Z when X = 405. So

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

Z = \frac{405 - 515}{100}

Z = -1.10

3 0
3 years ago
A minor league baseball team plays 101 games in a season. If the team won 14 more than twice as many games as they lost, how man
vagabundo [1.1K]
A minor league plays 101 games,
They win 14 more than twice as many as they lost.
How many wins and loses?

Okay, simple.
First, write a simple addition equation. In this case wins = w and losses = l.
l + w = 101.

Now, we have to figure out a way to make one of the terms the same term as the other, in this case we can change the terms of w to l.
l = l
w = 2l +14 (14 more than twice the amount)

Okay. So plug in the new amount for w.
l + 2l + 14 = 101. Great! we now have a simple equation. lets solve.
put similar terms together.
3l + 14 = 101
3l = 87
l = 29
So, we have 29 loses, and
w = 2(29) + 14
72 wins!
To check,
72 + 29 = 101, correct!

Hope this helps!

7 0
3 years ago
SEND HELP!!!!!!!!<br><br> (image is attached)
Mars2501 [29]

Answer:

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Step-by-step explanation:

we have to find the slope

y2-y1/x2-x1

3-2/23-22

1/1

y=1x+b

y-22 = 1(x-2) + b

y=x+20

5 0
3 years ago
11. What is the vertex of ZLMN?
astraxan [27]
ANSWER: (5,2)

according to the graph, the vertices of the
curve are 5 in abscissa and 2 in ordinate
hence the vertex (5,2)
3 0
2 years ago
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