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Salsk061 [2.6K]

2 years ago

15

The time that it takes to service a car is an exponential random variable with rate 1. If Lightning McQueen (L.M.) brings his ca

r in at time 0 and Sally Carrera (S.C) brings her car in at time t, what is the probability that S.C.'s car is ready before L.M.'s car? Assume that service times are independent and service begins upon arrival of the car. Be sure to: 1) define all random variables used, 2) explain how independence of service times plays a part in your solution, 3) show all integration steps. If both cars are brought in at time 0, with work starting on S.C.'s car only when L.M.'s car has been completely serviced, what is the probability that S.C.'s car is ready before time 2?

1 answer:

Paraphin [41]2 years ago

4 0

Answer:

Please find attached solution.

Step-by-step explanation:

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To plan the budget for next year a college must update its estimate of the proportion of next year's freshmen class that will ne

Naily [24]

Answer:

Null hypothesis: $p\leq 0.35$

Alternative hypothesis: $p > 0.35$

$z=\frac{0.447 -0.35}{\sqrt{\frac{0.35(1-0.35)}{150}}}=2.491$

$p_v =P(z>2.491)=0.0064$

So the p value obtained was a very low value and using the significance level assumed $\alpha=0.05$ we have $p_v$ so we can conclude that we have enough evidence to reject the null hypothesis, and we can said that at 5% of significance the proportion of applicants who request financial aid is significantly higher than 0.35

Step-by-step explanation:

Data given and notation

n=150 represent the random sample taken

X=67 represent the applicants who request financial aid

$\hat p=\frac{67}{150}=0.447$ estimated proportion of applicants who request financial aid

$p_o=0.35$ is the value that we want to test

$\alpha$ represent the significance level

z would represent the statistic (variable of interest)

$p_v$ represent the p value (variable of interest)

Concepts and formulas to use

We need to conduct a hypothesis in order to test the claim that the true proportion of applicants who request financial aid is higher than 0.35.:

Null hypothesis: $p\leq 0.35$

Alternative hypothesis: $p > 0.35$

When we conduct a proportion test we need to use the z statistic, and the is given by:

$z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}$ (1)

The One-Sample Proportion Test is used to assess whether a population proportion $\hat p$ is significantly different from a hypothesized value $p_o$ .

Calculate the statistic

Since we have all the info requires we can replace in formula (1) like this:

$z=\frac{0.447 -0.35}{\sqrt{\frac{0.35(1-0.35)}{150}}}=2.491$

Statistical decision

It's important to refresh the p value method or p value approach . "This method is about determining "likely" or "unlikely" by determining the probability assuming the null hypothesis were true of observing a more extreme test statistic in the direction of the alternative hypothesis than the one observed". Or in other words is just a method to have an statistical decision to fail to reject or reject the null hypothesis.

The next step would be calculate the p value for this test.

Since is a right tailed test the p value would be:

$p_v =P(z>2.491)=0.0064$

So the p value obtained was a very low value and using the significance level assumed $\alpha=0.05$ we have $p_v$ so we can conclude that we have enough evidence to reject the null hypothesis, and we can said that at 5% of significance the proportion of applicants who request financial aid is significantly higher than 0.35

5 0

2 years ago

What is the distance from the origin of point P graphed on the complex plane below?

ZanzabumX [31]

Answer:

b) √29

Step-by-step explanation:

Given: The origin is (0, 0), the point P is (2, -5).

We need to use the distance formula.

Distance formula = $\sqrt{(x2 -x1)^2 + (y2 - y1)^2} \\$

Here x2 = 2, x 1 = 0, y1 =0, y2 = -5

Distance = $\sqrt{(2 -0)^2 + (-5 - 0)^2}$

= $\sqrt{2^2 + (5)^2}$

= √(4 + 25)

= √29

The answer is b) √29

Hope you will understand the concept.

Thank you.

7 0

2 years ago

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Which of the following is the radical expression of a to the four ninths power?

iogann1982 [59]

Step-by-step explanation:

$\sqrt[n]{a^m}=a^\frac{m}{n}\\\\\large\huge\boxed{a^\frac{4}{9}=\sqrt[9]{a^4}}$

3 0

2 years ago

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A turtle walks 7/8 of a mile in 50 minutes. What is the unit rate when the turtle’s speed is expressed in miles per hour?

yKpoI14uk [10]

Answer:

21/20

Step-by-step explanation:

a) One hour is equivalent to 60 minutes.

So we can multiply 50 minutes by the fraction $\frac{1 hour}{60 minutes}$ , so we could convert 50 minutes to hours.

It is:

$50 minutes * \frac{1 hour}{60 minutes}=\frac{50}{60}hours$

If we simplify the fraction, we have:

$50 minutes = \frac{5}{6}hours$

b) In order to express the turtle's speed in miles per hour, we have to divide

$\frac{7}{8}miles$ by $\frac{5}{6}hours$

So:

$\frac{\frac{7}{8}miles }{\frac{5}{6}hours }$

We simplify the expression by multiplying 7 mile by 6 and 8 by 5 hours:

$\frac{\frac{7}{8}miles }{\frac{5}{6}hours}=\frac{42 miles}{40 hours} =\frac{21 miles}{20 hours}$

4 0

2 years ago

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Two of the steps in the derivation of the quadratic formula are shown below. Step 6: StartFraction b squared minus 4 a c Over 4

sergeinik [125]

Answer:

Step-by-step explanation:

From the step given step 6

(b² — 4ac) / 4a² = (x + b/2a)²

Mistake in question it is (x + b/2a)²

Step 7 given

±√(b² —4ac) /2a = x + b/2a

Mistake in question it is over 2a and not 1a.

1. The step taken from step 6 to step 7 is taking square roots of both sides

(b² — 4ac) / 4a² = (x + b/2a)²

Taking square of both sodes

√(b²—4ac) / √4a² = √(x + b/2a)²

√(b²—4ac) / 2a = x + b/2a

This is the required step 7.

Now, subtracting b/2a from both sides

√(b²—4ac) / 2a - b/2a= x + b/2a -b/2a

√(b²—4ac) / 2a — b/2a = x

(√(b²—4ac) — b)/2a = x

x = [—b ± √(b²—4ac)] / 2a

So, this is the required formula method

The discriminant is D = b²—4ac.

6 0

2 years ago

Read 2 more answers