MATHEMATICS COLLEGE

The following measurements were recorded for the drying time, in hours, of a certain brand of latex paint: 3.4, 2.5, 4.8, 2.9, 3.6, 2.8, 3.3, 5.6, 3.7, 2.8, 4.4, 4.0, 5.2, 3.0, 4.8. Assuming that the measurements represent a random sample from a normal population, find a 95% prediction interval for the drying time for the next trial of the paint.

Answers

Answer 1

Answer:

Answer:

The 95% confidence interval for the mean is (3.249, 4.324).

We can predict with 95% confidence that the next trial of the paint will be within 3.249 and 4.324.

Step-by-step explanation:

We have to calculate a 95% confidence interval for the mean.

As the population standard deviation is not known, we will use the sample standard deviation as an estimation.

The sample mean is:

$M=(1)/(15)\sum_(i=1)^(15)(3.4+2.5+4.8+2.9+3.6+2.8+3.3+5.6+3.7+2.8+4.4+4+5.2+3+4.8)\n\n\n M=(56.8)/(15)=3.787$

The sample standard deviation is:

$s=\sqrt{(1)/((n-1))\sum_(i=1)^(15)(x_i-M)^2}\n\n\ns=\sqrt{(1)/(14)\cdot [(3.4-(3.787))^2+(2.5-(3.787))^2+(4.8-(3.787))^2+...+(4.8-(3.787))^2]}\n\n\n$ $s=\sqrt{(1)/(14)\cdot [(0.15)+(1.66)+(1.03)+...+(1.03)]}$

$s=\sqrt{(13.197)/(14)}=√(0.9427)\n\n\ns=0.971$

We have to calculate a 95% confidence interval for the mean.

The population standard deviation is not known, so we have to estimate it from the sample standard deviation and use a t-students distribution to calculate the critical value.

The sample mean is M=3.787.

The sample size is N=15.

When σ is not known, s divided by the square root of N is used as an estimate of σM:

$s_M=(s)/(√(N))=(0.971)/(√(15))=(0.971)/(3.873)=0.2507$

The t-value for a 95% confidence interval is t=2.145.

The margin of error (MOE) can be calculated as:

$MOE=t\cdot s_M=2.145 \cdot 0.2507=0.538$

Then, the lower and upper bounds of the confidence interval are:

$LL=M-t \cdot s_M = 3.787-0.538=3.249\n\nUL=M+t \cdot s_M = 3.787+0.538=4.324$

The 95% confidence interval for the mean is (3.249, 4.324).

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How to solve -2x-10x12=18

Answers

Answer:

x = −69

Step-by-step explanation:

1: Simplify

−2x−(10)(12)=18

−2x+−120=18

−2x−120=18

2: Add 120 to both sides.

−2x−120+120=18+120

−2x = 138

3: Divide both sides by -2.

-2x ÷ -2 = 138 ÷ -2

x = −69

Answer:

x=-69

Step-by-step explanation:

PLEASE PLEASE PLEASE HELP. This is a geometry worksheet.

Answers

Answer:

where's the question?

An object is translated by (x-2, y-6). If one point in the pre-image has the coordinates (-3, 7), what would be the coordinates of its image? (-1,7) O (-5,1) O(-9,5) O (-1, 13)

Answers

Answer:(-5,1)

Step-by-step explanation:! X= -3 so -3-4= -7, Y= 7 so 7+2=9, So the coordinates will be (-7,9) I hope that I could help you

Weights of babies at the local community hospital have a distribution that is approximately normal with a mean weight of 7.43 pounds and a standard deviation of 1.25 pounds. A premature baby can be classified as being less than 5.51 pounds. A. Find the probability of a randomly selected baby weighing less than 5.51 pounds. B. If 25 babies are randomly selected, what is the probability that their weight will be less than 5.51 pounds?

Answers

Answer:

Step-by-step explanation:

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The area of the square is 36 cm. 2 what is the formula that shows the length or side b

Answers

Answer:

36=b^2 or b=the square root of 36

Step-by-step explanation:

The sides of a square are all equal in length. To find the area of a square you can multiply the two sides together. Considering that they are the same length, you can just square one of the side lengths to get your answer. To find a side length you can take the square root of the area.

Answer:

Step-by-step explanation:

b · b = 36

Alex buys six equally priced candy bars for $9:00 what is the unit rate?