Please Help!!! Braniest!!!!

A quality analyst of a tennis racquet manufacturing plant investigates if the length of a junior's tennis racquet conforms to th

Burka [1]

Answer:

Confidence interval : $21.506$ to $24.493$

Step-by-step explanation:

A quality analyst selects twenty racquets and obtains the following lengths:

21, 25, 23, 22, 24, 21, 25, 21, 23, 26, 21, 24, 22, 24, 23, 21, 21, 26, 23, 24

So, sample size = n =20

Now we are supposed to find Construct a 99.9% confidence interval for the mean length of all the junior's tennis racquets manufactured at this plant.

Since n < 30

So we will use t-distribution

Confidence level = 99.9%

Significance level = α = 0.001

Now calculate the sample mean

X=21, 25, 23, 22, 24, 21, 25, 21, 23, 26, 21, 24, 22, 24, 23, 21, 21, 26, 23, 24

Sample mean = $\bar{x}=\frac{\sum x}{n}$

Sample mean = $\bar{x}=\frac{21+25+23+22+24+21+25+21+23+ 26+ 21+24+22+ 24+23+21+ 21+ 26+23+ 24}{20}$

Sample mean = $\bar{x}=23$

Sample standard deviation = $\sqrt{\frac{\sum(x-\bar{x})^2}{n-1}}$

Sample standard deviation = $\sqrt{\frac{(21-23)^2+(25-23)^2+(23-23)^2+(22-23)^2+(24-23)^2+(21-23)^2+(25-23)^2+(21-23)^2+(23-23)^2+(26-23)^2+(21-23)^2+(24-23)^2+(22-23)^2+(24-23)^2+(23-23)^2+(21-23)^2+(21-23)^2+(26-23)^2+(23-23)^2+(24-23)^2}{20-1}}$

Sample standard deviation= s = $1.72$

Degree of freedom = n-1 = 20-1 -19

Critical value of t using the t-distribution table $t_{\frac{\alpha}{2}$ = 3.883

Formula of confidence interval : $\bar{x} \pm t_{\frac{\alpha}{2}} \times \frac{s}{\sqrt{n}}$

Substitute the values in the formula

Confidence interval : $23 \pm 1.73 \times \frac{1.72}{\sqrt{20}}$

Confidence interval : $23 -3.883 \times \frac{1.72}{\sqrt{20}}$ to $23 + 3.883 \times \frac{1.72}{\sqrt{20}}$

Confidence interval : $21.506$ to $24.493$

Hence Confidence interval : $21.506$ to $24.493$

3 0

4 years ago

Read 2 more answers

I need helpppp plssss anyone I’m not the best at math :/

Ulleksa [173]

Answer:

C

Step-by-step explanation:

7 0

3 years ago

Person A can paint the neighbor's house 6 times as fast as Person B. The year A and B worked together it

uranmaximum [27]

Person A takes 2.3 days to paint the house working alone

Person B takes 13.8 days to paint the house working alone

<em><u>Solution:</u></em>

Let "x" be the number of days it takes person A to paint the house

Person A can paint the neighbor's house 6 times as fast as Person B

Therefore.

Number of days it takes person B to paint the house = 6x

Their rates of painting are added to get the rate working together

$\frac{\text{1 house}}{\text{x days}} + \frac{\text{1 house}}{\text{6x days}} = \frac{\text{1 house}}{\text{2 days}}$

$\frac{1}{x} + \frac{1}{6x} = \frac{1}{2}\\\\\frac{1 \times 6}{6x} + \frac{1}{6x} = \frac{1}{2}\\\\\frac{7}{6x} = \frac{1}{2}\\\\\ x = \frac{7}{3}= 2.3$

Thus person A takes 2.3 days to paint the house working alone

Person B = 2x = 6(2.3) = 13.8

Thus person B takes 13.8 days to paint the house working alone

3 0

3 years ago

Which sequence is arithmetic?

MissTica

Answer:

11, 14, 17, 20

Step-by-step explanation:

An arithmetic sequence has a common difference d between consecutive terms.

Consider 2, 6, 18, 54

6 - 2 = 4, 18 - 6 = 12, 54 - 18 = 36 ← no common difference, not arithmetic

Consider 3, 6, 12, 24

6 - 3 = 3, 12 - 6 = 6, 24 - 12 = 12 ← no common difference, not arithmetic

Consider 11, 14, 17, 20

14 - 11 = 3, 17 - 14 = 3, 20 - 17 = 3 ← common difference of 3, so arithmetic

Consider 7, 11, 13, 18

11 - 7 = 4, 13 - 11 = 2, 18 - 13 = 5 ← no common difference, not arithmetic

The arithmetic sequence is 11, 14, 17, 20

3 0

3 years ago

What is 1.9 inches to the nearest fourth inch?

Reptile [31]

Yeah I got told you her that you didn't know what about it your it iohappened

6 0

3 years ago