Ask question

Ask question

All categories

Nimfa-mama [501]

3 years ago

15

How many commuters must be randomly selected to estimate the mean driving time of Chicago commuters? We want 95% confidence that

the sample mean is within 3 minutes of the population mean, and the population standard deviation is known to be 12 minutes.

2 answers:

Oduvanchick [21]3 years ago

8 0

Answer:

61 commuters must be randomly selected to estimate the mean driving time of Chicago commuters.

Step-by-step explanation:

zimovet [89]3 years ago

6 0

Answer:

61 commuters must be randomly selected to estimate the mean driving time of Chicago commuters.

Step-by-step explanation:

Given : We want 95% confidence that the sample mean is within 3 minutes of the population mean, and the population standard deviation is known to be 12 minutes.

To find : How many commuters must be randomly selected to estimate the mean driving time of Chicago commuters?

Solution :

At 95% confidence the z-value is z=1.96

The sample mean is within 3 minutes of the population mean i.e. margin of error is E=3 minutes

The population standard deviation is s=12 minutes

n is the number of sample

The formula of margin of error is given by,

$E=\frac{s\times z}{\sqrt{n}}$

Substitute the value in the formula,

$3=\frac{12\times 1.96}{\sqrt{n}}$

$3=\frac{23.52}{\sqrt{n}}$

$\sqrt{n}=\frac{23.52}{3}$

$\sqrt{n}=7.84$

Squaring both side,

$n=61.4656$

Therefore, 61 commuters must be randomly selected to estimate the mean driving time of Chicago commuters.

You might be interested in

An exterior angle of a regular polygon cannot have the measure Select one: a. 90 b. 120 c. 50 d. 40 e. 30

Otrada [13]

Answer: c. 50

Step-by-step explanation:

1. By definition, when you add the exterior angles of a regular polygon, you obtain 360 degrees and the number of sides of that polygon can be calculated by dividing 360 degrees by the measure of the exterior angle of it.

2. As you know, the number of sides cannot be fractions, therefore, if you make the folllowing division:

360°/50°=36/5

You obtain a fraction.

3. Then, an exterior angle of a regular polygon cannot have the measure is 50°.

7 0

3 years ago

Read 2 more answers

PLEASEEEE HELPP MEEE WITHHH NUMBERSSS 9 AND 10

den301095 [7]

Answer:

9) <4=89

10) x=35

Step-by-step explanation:

9) 52+39=91

180-91=89

10) 2x+x+13+62=180

3x+75=180

-75 -75

3x=105

105/3=35

4 0

3 years ago

Read 2 more answers

Record sales are increasing by 5% each year. If 800,000 records were sold this year, what will annual sales be in 3 years?

Olenka [21]

Answer:

120000

Step-by-step explanation:

3 0

2 years ago

What is 1995298 rounded to the nearest 10000

Setler [38]

100,000.......Please mark brainliest....

3 0

3 years ago

Read 2 more answers

Find the sum of the positive integers less than 200 which are not multiples of 4 and 7

taurus [48]

Answer:

$12942$ is the sum of positive integers between $1$ (inclusive) and $199$ (inclusive) that are not multiples of $4$ and not multiples $7$ .

Step-by-step explanation:

For an arithmetic series with:

$a_1$ as the first term,
$a_n$ as the last term, and
$d$ as the common difference,

there would be $\displaystyle \left(\frac{a_n - a_1}{d} + 1\right)$ terms, where as the sum would be $\displaystyle \frac{1}{2}\, \displaystyle \underbrace{\left(\frac{a_n - a_1}{d} + 1\right)}_\text{number of terms}\, (a_1 + a_n)$ .

Positive integers between $1$ (inclusive) and $199$ (inclusive) include:

$1,\, 2,\, \dots,\, 199$ .

The common difference of this arithmetic series is $1$ . There would be $(199 - 1) + 1 = 199$ terms. The sum of these integers would thus be:

$\begin{aligned}\frac{1}{2}\times ((199 - 1) + 1) \times (1 + 199) = 19900 \end{aligned}$ .

Similarly, positive integers between $1$ (inclusive) and $199$ (inclusive) that are multiples of $4$ include:

$4,\, 8,\, \dots,\, 196$ .

The common difference of this arithmetic series is $4$ . There would be $(196 - 4) / 4 + 1 = 49$ terms. The sum of these integers would thus be:

$\begin{aligned}\frac{1}{2}\times 49 \times (4 + 196) = 4900 \end{aligned}$

Positive integers between $1$ (inclusive) and $199$ (inclusive) that are multiples of $7$ include:

$7,\, 14,\, \dots,\, 196$ .

The common difference of this arithmetic series is $7$ . There would be $(196 - 7) / 7 + 1 = 28$ terms. The sum of these integers would thus be:

$\begin{aligned}\frac{1}{2}\times 28 \times (7 + 196) = 2842 \end{aligned}$

Positive integers between $1$ (inclusive) and $199$ (inclusive) that are multiples of $28$ (integers that are both multiples of $4$ and multiples of $7$ ) include:

$28,\, 56,\, \dots,\, 196$ .

The common difference of this arithmetic series is $28$ . There would be $(196 - 28) / 28 + 1 = 7$ terms. The sum of these integers would thus be:

$\begin{aligned}\frac{1}{2}\times 7 \times (28 + 196) = 784 \end{aligned}$ .

The requested sum will be equal to:

the sum of all integers from $1$ to $199$ ,
minus the sum of all integer multiples of $4$ between $1\!$ and $199\!$ , and the sum integer multiples of $7$ between $1$ and $199$ ,
plus the sum of all integer multiples of $28$ between $1$ and $199$ - these numbers were subtracted twice in the previous step and should be added back to the sum once.

That is:

$19900 - 4900 - 2842 + 784 = 12942$ .

8 0

3 years ago