MATHEMATICS COLLEGE

According to the Sydney Morning Herald, 40% of bicycles stolen in Holland are recovered. (In contrast, only 2% of bikes stolen in New York City are recovered.) Find the probability that, in a sample of 6 randomly selected cases of bicycles stolen in Holland, exactly 2 out of 6 bikes are recovered. Find the nearest answer.

Answers

Answer 1

Answer:

Answer:

0.31104

Step-by-step explanation:

Given that according to the Sydney Morning Herald, 40% of bicycles stolen in Holland are recovered.

If X represents the number of bicyles stolen in Sydney, X is binomial

because each cycle to be stolen is independent of the other.

Also there are two outcomes

n = 6, p = 0.40

Required probability = the probability that, in a sample of 6 randomly selected cases of bicycles stolen in Holland, exactly 2 out of 6 bikes are recovered

==P(X=2)

= $6C2 (0.4)^2 (0.6)^4\n= 15(0.16)(0.6)^4\n=0.31104$

Answer 2

Answer:

Answer:

Probability that exactly 2 out of 6 bikes are recovered is 0.31.

Step-by-step explanation:

We are given that according to the Sydney Morning Herald, 40% of bicycles stolen in Holland are recovered.

Also, there is a sample of 6 randomly selected cases of bicycles stolen in Holland.

The above situation can be represented through Binomial distribution;

$P(X=r) = \binom{n}{r}p^(r) (1-p)^(n-r) ; x = 0,1,2,3,.....$

where, n = number of trials (samples) taken = 6 cases of bicycles

r = number of success = exactly 2

p = probability of success which in our question is % of bicycles

stolen in Holland that are being recovered, i.e; 40%

LET X = Number of bikes recovered

So, it means X ~ $Binom(n=6, p=0.40)$

Now, Probability that exactly 2 out of 6 bikes are recovered is given by = P(X = 2)

P(X = 2) = $\binom{6}{2}0.40^(2) (1-0.40)^(6-2)$

= $15 * 0.40^(2) * 0.60^(4)$

= 0.31

Therefore, Probability that, in a sample of 6 randomly selected cases of bicycles stolen in Holland, exactly 2 out of 6 bikes are recovered is 0.31.

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-8r –9 > -21...............

Answers

Answer:

r < 3/2 or r < 1.5

Step-by-step explanation:

-8r - 9 > 21

-8r > -21 +9

-8r > -12

divide both sides by -8

= r < 3/2 or 1.5

Luis drew a rectangle on his paper that was 112 cm by 16 cm. What is the area and the perimeter of the rectangle that Luis drew on his paper?PLEASE HELP ME OUT!! THIS IS DUE TODAY!

Answers

Answer:

Area - 1,792 Perimeter-256

Step-by-step explanation:

Area

length x width 112 x 16 =1,792

Perimeter

length x2 width x2 then add answers together

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We wish to study the quality of our production line. We take a random sample of 1000 widgets from our line. A quality rating was determined for each of the 1000 widgets, and the average quality rating in the sample was 4. The sample standard deviation was 0.5. Also, 6 of the 1000 widgets were found to be defective.Estimate the average quality rating for widgets from our production line, and include the uncertainty in this estimate in the form, a ± b.

Answers

Answer:

Average quality rating was 4.54+-0.00549

Final answer:

The estimate for the average quality rating from the production line, given this sample, is 4, with a degree of uncertainty expressed by a 95% confidence interval of 4 ± 0.031. The confidence interval represents a range whereby we can be 95% confident that the true mean lies within.

Explanation:

Since you have the average (mean) quality rating and standard deviation from a sample size of 1000 widgets, we can use these statistics to establish an estimate for the entire production line. The estimate of the average quality rating is given as 4. However, to account for the uncertainty of our estimate due to it being based upon a sample rather than the entire population, we use the concept of a confidence interval.

The formula for a confidence interval is mean ± z* (standard deviation/sqrt(n)), where z is a z-score corresponding to our desired level of confidence. For simplicity, we can use a z-score of 1.96 to represent a confidence level of 95%.

Therefore, the uncertainty in this estimate (at 95% confidence) is calculated as:1.96 * (0.5/sqrt(1000)), approximately equal to 0.031. So the confidence interval for the average quality of widgets is 4 ± 0.031.

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Answers

Answer:

<BAE is congruent to <DAC (first choice)

Step-by-step explanation:

Triangle ACD has three angles: <DAC, <ACD, <ADC

Triangle ABE has three angles: <BAE, <AEB, <ABE

Angles ACD, ADC, AEB and ABE are all different angles. Look them up in the figure, and you'll see they are 4 different angles.

Angles BAE and DAC are the same angle.

Answer: <BAE is congruent to <DAC (first choice)

An oil company fills 1/12 of a tank in 1/3 hour. At this rate, which expression can be used to determine how long will it take for the tank to fill completely? a. 1/12 x 3 hours
b. 1/3 x 12 hours
c. 1/3 x 1/12 hour
d. 3 x 12 hours

Answers

Selection B is appropriate.

_____
It takes 12 times as long to fill the whole tank as it does to fill 1/12 of the tank.
.. 12 * (1/3 hour) = (1/3)*12 hour

Answer: b . $(1)/(3)*12$ hours