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.

6 0

2 years ago

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8/5 ( 2x + 13 ) - 3 = 22

Alona [7]

Answer:

$x = \frac{21}{16}$ = 1 5/16

[/tex] 1 \frac{5}{16}[/tex]

Step-by-step explanation:

$\frac{8}{5} (2x + 13) - 3 = 22$

Expand

$\frac{16}{5} x + \frac{104}{5} - 3 = 22 \\ \frac{16}{5} x + \frac{89}{5} = 2$

Collect like terms and simplify

$\frac{16}{5} x = 22 - \frac{89}{5} \\ \frac{16}{5} x = \frac{21}{5}$

Cross Multiply

$80x = 105$

Divide both sides of the equation by 80

$\frac{80x}{80} = \frac{105}{80} \\ x = \frac{21}{16}$

5 0

3 years ago