1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
VMariaS [17]
3 years ago
8

The accompanying data represent the miles per gallon of a random sample of cars with a​ three-cylinder, 1.0 liter engine.a. Comp

ute the​ z-score corresponding to the individual who obtained 37.8 miles per gallon. Interpret this result.b. Determine the quartiles.c. Compute and interpret the interquartile​ range, IQR.d. Determine the lower and upper fences. Are there any​outliers?31.5 36.0 37.8 38.5 40.1 42.234.2 36.2 38.1 38.7 40.6 42.534.7 37.3 38.2 39.5 41.4 43.435.6 37.6 38.4 39.6 41.7 49.3The​ z-score corresponding to the individual is ____ and indicates that the data value is ___ standard​ deviation(s) ______ the _____.

Mathematics
1 answer:
Kobotan [32]3 years ago
4 0

Answer:

1). Z score = 1.464733

Mean = 38.87917

Standard deviation = 3.609405

2). Quartiles:

Q1 = 37.025

Q2 = 38.450

Q3 = 40.800

3). IQR = 3.775

4).

CI (lower fence) = 37.4351

CI (upper fence) =  40.32323

5). There is outlier in the data set. Please see attached box plot for evidence.

Step-by-step explanation:

1). By Z score, we mean:

Z = \frac{\bar{x} - \mu}{\frac{\sigma}{\sqrt{n}}},

where:

x-bar ==> mean(g) = 38.87917

\mu = 37.80

standard deviation = 3.609405

sample size (n) = 24.

2). By quantile, we mean:

Q = L + (i*(n/4) - Cf)*c

Where L is the lower class limit of the quartile class

Cf is the cumulative frequency before the quartile class

c  is the class size.

3) . IQR = Q3 - Q1

4). CI = \mu \pm *Z_{\alpha/2} \frac{\sigma}{\sqrt{n}},

Where Z_{\alpha/2}  ==> 1.96

In order to replicate and obtain the result, please use the R code below:

g = c(31.5, 36.0, 37.8, 38.5, 40.1, 42.2,34.2, 36.2, 38.1, 38.7, 40.6, 42.5,34.7, 37.3, 38.2, 39.5,  

41.4, 43.4,35.6, 37.6, 38.4, 39.6, 41.7, 49.3)

boxplot(g)

Z = (mean(g) - 37.8)/(sd(g)/sqrt(length(g)))

mean(g)

quantile(g)

IQR(g)

CIl = mean(g) - 1.96*(sd(g)/sqrt(length(g)))

CIU = mean(g) + 1.96*(sd(g)/sqrt(length(g)))

You might be interested in
Paula was standing on top of a cliff 35 feet above sea level. She watched her friend Juan jump from the cliff to a depht of 12 f
DIA [1.3K]
23 feet, I think but I'm not 100% sure
6 0
3 years ago
After sales tax, a $600 antique clock costs $642. What is the sales tax percentage?
LenKa [72]

well, clearly the tax is the added 42 bucks, so hmmm if we take 600 to be the 100%, how much is 42 off of it in percentage?

\begin{array}{ccll} amount&\%\\ \cline{1-2} 600 & 100\\ 42& x \end{array} \implies \cfrac{600}{42}=\cfrac{100}{x}\implies \cfrac{100}{7}=\cfrac{100}{x} \\\\\\ 100x=700\implies x=\cfrac{700}{100}\implies x=7

5 0
2 years ago
Read 2 more answers
What percent of 48 is 18
arsen [322]
To find the percent you take 18 and divide it by 48, so you get 9/24 or 3/8, by using calculator you get .375 which is 37.5% then you multiply by 100 to convert a decimal to a percentage.
6 0
3 years ago
PLEASE HELP! NO ONE HAS BEEN HELPING WITH MY QUESTIONS SO IT WOULD MEAN A LOT IF YOU DID!
kvv77 [185]

Answer:

80 m²

Step-by-step explanation:

The area (A) of a trapezoid is calculated as

A = \frac{1}{2} h (a + b)

where h is the perpendicular height between bases and a, b are the bases

Here h = 8, a = 14 and b = 6, thus

A = \frac{1}{2} × 8 × (14 + 6) = 4 × 20 = 80 m²

3 0
3 years ago
Marcus earns $8.40 per hour. He works for 26 hours each week, 48 weeks each year. If he earns over $10,000, then Marcus has to p
MAVERICK [17]

We have been given that Marcus works for 26 hours each week and 48 weeks each year.

Thus in a year he works for 26 \times 48 = 1248 hours.

Now, we have been given that Marcus earns $8.40 per hour.

Therefore, in 1248 hours, he earns

1248 \times 8.40\\
\\
=\$ 10483.2

Marcus has to pay tax if he earns more than $10,000. Now we have calculated that he earns $ 10483.2  which is higher than $10,000.

Therefore, Marcus has to to pat tax.

6 0
3 years ago
Read 2 more answers
Other questions:
  • Can someone help me with this question please
    15·1 answer
  • What’s the area of a square with a diagonal of 8in
    10·2 answers
  • A souvenier maker wants to create a scale model of threiffel tower. The effiel tower is 324 meters tall and has a base with dime
    8·1 answer
  • Given ƒ(x) = −15x − 13, find x when ƒ(x) = −28
    14·1 answer
  • HOW MANY TENTHS ARE IN 13.58
    12·2 answers
  • Write a rule for the sequence 2,4,8,16
    5·1 answer
  • Least to greatest djjzhxjxhxjxjx
    14·1 answer
  • 5 Marta designs a logo for her mother's business,
    8·1 answer
  • Brainiest for a roux card (don't have to but if you want)
    12·1 answer
  • What is 2w + 9( w + 10 )
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!