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Leya [2.2K]
3 years ago
9

The Scottsdale fire department aims to respond to fire calls in 4 minutes or less, on average. Response times are normally distr

ibuted with a standard deviation of 1 minute. Would a sample of 18 fire calls with a mean response time of 4 minutes 30 seconds provide sufficient evidence to show that the goal is not being met at α = .01?
Mathematics
1 answer:
IgorC [24]3 years ago
3 0
<h2><u>Answer with explanation</u>:</h2>

Let \mu be the population mean.

As per given , we have

H_0:\mu \leq4\\\\ H_a: \mu >4

Since the alternative hypothesis is right-tailed , so the test is a right-tailed test.

Also, population standard deviation is given \sigma=1 , so we perform one-tailed z-test.

Test statistic : z=\dfrac{\overline{x}-\mu}{\dfrac{\sigma}{\sqrt{n}}}

, where \mu = Population mean

\sigma = Population standard deviation

n= sample size

\overline{x} = Sample mean

For n= 18 , \overline{x}=4.50 , \sigma=1 , \mu =4, we have

z=\dfrac{4.5-4}{\dfrac{1}{\sqrt{18}}}\approx2.12

P-value (for right tailed test): P(z>2.12) = 1-P(z≤ 2.12)  [∵ P(Z>z)=1-P(Z≤z)]\

=1- 0.0340=0.9660

Decision : Since P-value(0.9660) > Significance level (0.01), it means we are failed to reject the null hypothesis.

[We reject null hypothesis if p-value is larger than the significance level . ]

Conclusion : We do not have sufficient evidence to show that the goal is not being met at α = .01 .

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In the figure on the right, Triangle EFG is congruent to Triangle LMN. Find the value of x. Then describe the Transformations th
Reptile [31]

Answer:

Step-by-step explanation:

ΔEFG ≅ΔLMN

Therefore,  MN = FG    { corresponding part of congruence triangle}

x + 3 = 13

x = 13 - 3

x = 10 cm

3 0
3 years ago
Read 2 more answers
1. In the diagram below , lines a and b are paraller and cut by traversal, t of angle 3 is 120 degrees, find the measure of angl
Lelu [443]

the complete question in the attached figure

<span>1. In the diagram below , lines a and b are parallel and cut by traversal, t of angle 3 is 120 degrees, find the measure of angle 7.

 </span>∡3=∡7------------- >  <span>corresponding angles
the answer is </span>∡7=120 degrees

<span>2. in the diagram below , lines a and b are parallel and cut by traversal, t of angle 2 is 50 degrees, find the measure of angle 8.

</span>∡2=∡8------------- >  <span>alternate exterior angles
</span>
the answer is ∡8=50 degrees

<span>3. In the diagram below , lines a and b are parallel and cut by traversal, t of angle 6 is 50 degrees, find the measure of angle 4.

</span>∡6=∡4------------- >  <span>alternate interior angles

</span>the answer is ∡4=50 degrees

6 0
3 years ago
Which linear inequality is represented by the graph? y ≤ 1/2x + 2 y ≥ 1/2x + 2 y ≤ 2/3x + 2 y ≥ 2/3x + 2
patriot [66]
Post the graph and I can help
6 0
3 years ago
Read 2 more answers
Please Solve this, it would be extremely helpful for me.
Sidana [21]

Answer:

Step-by-step explanation:

1) ΔCPD & ΔEPF

∠CPD = ∠EPF   { Vertically opposite angles}

∠CDP = ∠PFE {CD║EF, FD is transversal, Alternate interior angles are equal}

ΔCPD ≈ΔEPF  {AA criteria for similarity }

\frac{DC}{EF} =\frac{PC}{EP}\\\\\\\frac{27}{EF}=\frac{15}{7.5}\\\\

Cross multiply

EF * 15 = 27 * 7.5

EF =\frac{27*7.5}{15}\\\\

EF = 27 * 0.5

EF = 13.5 cm

ii) EF // AB, so Triangles ACB & ECF are similar triangles

\frac{AB}{EF}=\frac{AC}{EC}\\\\\frac{22.5}{13.5}=\frac{AC}{22.5}

AC= \frac{22.5*22.5}{13.5}\\\\AC=37.5 cm

AC = 37.5 cm

6 0
3 years ago
Elisa is nearing graduation. She just met with her counselor and he showed her this information.
Arada [10]

Answer: $14,000

Step-by-step explanation:

Given the following :

Room & Board = $11,500

Work - study = $8000

Grant & scholarship = $9500

Tuition fee = $9500

If she pays balance with a student loan, how much will she need to borrow:

Elisha's bill:

Tuition fee and room and board

($9500 + $11500) = $21,000

Elisha's earning:

Work - study and scholarship & grant

($8000 + $9500) = $17500

Therefore,

Amount to borrow per year :

$21,000 - $17,500 = $3500

For four years :

4 × $3,500 = $14,000

8 0
3 years ago
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