Mathematics, 18.11.2019 22:31 Cleotilde14151

An environmental agency worries that many cars may be violating clean air emissions standards. the agency hopes to check a sample of vehicles in order to estimate that percentage with a margin of error of 3% and 90% confidence. to gauge the size of the problem, the agency first picks 40 cars and finds 8 with faulty emissions systems. how many should be sampled for a full investigation?

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Answer from: SophieStar15

482 cars

Step-by-step explanation:

The formula to find the sample size is given by :-

$n= p(1-p)(\dfrac{z_{\alpha/2}}{E})^2$

, where p is the prior estimate of population proportion.

$z_{\alpha/2}$ = Two-tailed z-value for $\alpha$ (significance level).

E= Margin of error .

Given : Margin of error = 3% = 0.03

Confidence level = 90%=0.90

$\alpha=1-0.90=0.10$

By z-value table : $z_{\alpha/2}=z_{0.05}=1.645$

To gauge the size of the problem, the agency first picks 40 cars and finds 8 with faulty emissions systems.

Then , the prior estimate of population proportion of faulty emissions systems = $p=\dfrac{8}{40}=0.2$

Then, the required sample size would be :

$n= 0.2(1-0.2)(\dfrac{1.645}{0.03})^2$

n=0.16(3006.6944)

$n=481.071104\approx482$

Hence, 482 cars should be sampled for a full investigation.

Answer from: Quest

2 and 1.

step-by-step explanation:

plug in each answer. 0 doesn't work, 1 does. so does 2. 4 doesn't:

0 = 1 is not true.

2 = 2 is true.

4 = 4 is true.

8 = 16 is not true.

hope this !

Answer from: Quest

if gloria has "carry over" minutes, (that is, any minutes paid for but not used in a month can be applied to her payment for minutes in the next month,) her total usage for the three months is: total minutes = 320 + 243 + 489 = 1052 minutes number of 200 minute blocks = 1052/200 = 5 r52 (that is 5 with a remainder of 52) rounding up the number of 200 minute blocks gives her usage for the three months as 6 blocks. the cost for six blocks is 6 x $25 = $150 she also has 200 - 52 or 148 carry over minutes if gloria pays each month and unused minutes are lost, applying the rounding up procedure to each month gives: first month usage of 320 minutes rounds up to 2 blocks of 200 minutes for a payment of 2 x $25 = $50 second month usage of 243 minutes rounds up to 2 blocks of 200 minutes for a payment of 2 x $25 = $50 third month usage of 489 minutes rounds up to 3 blocks of 200 minutes for a payment of 3 x $25 = $75 total payments for the three months are $50 + $50 + $75 = $175 get the plan with carry over minutes!

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