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anygoal [31]
3 years ago
14

A random sample of 16 one-kilogram sugar packets is obtained and the actual weights of the packets are measured. The sample mean

is x 1.053  kg, and the sample standard deviation is s 0.058  kg. Assume that the weights are approximately normally distributed. A) Construct a 99% two-sided confidence interval for the average sugar packet weight.
Mathematics
1 answer:
elena55 [62]3 years ago
3 0

Answer:

The 99% two-sided confidence interval for the average sugar packet weight is between 0.882 kg and 1.224 kg.

Step-by-step explanation:

We are in posession of the sample's standard deviation, so we use the student's t-distribution to find the confidence interval.

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 16 - 1 = 15

99% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 35 degrees of freedom(y-axis) and a confidence level of 1 - \frac{1 - 0.99}{2} = 0.905([tex]t_{995}). So we have T = 2.9467

The margin of error is:

M = T*s = 2.9467*0.058 = 0.171

In which s is the standard deviation of the sample.

The lower end of the interval is the sample mean subtracted by M. So it is 1.053 - 0.171 = 0.882kg

The upper end of the interval is the sample mean added to M. So it is 1.053 + 0.171 = 1.224 kg.

The 99% two-sided confidence interval for the average sugar packet weight is between 0.882 kg and 1.224 kg.

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In a triangle, the sum of the measures of the first two angles is 12 less than the measure of the third angle. In addition, the
USPshnik [31]

The measure of the three angles are  56, 28 , 192 degree

<h3>What is a Triangle ?</h3>

A triangle is a polygon with three sides , three vertices an three angles.

It is given to make system of equations

Let the measure of the first , second and third angle be x, y and z

the sum of the measures of the first two angles is 12 less than the measure of the third angle.

x +y = z -12  ----1

the measure of the first angle is twice as big as the measure of the second angle.

x = 2y

Now equation 1 will be

z - 3y = 12

x +y+z = 180

2y +y +z = 180

3y +z = 180 ----2

z - 3y = 12------3

On solving the system of equation 1, 2

2z = 192

z= 96 degree

3y = 180-96

y = 28

x = 56

Therefore the measure of the three angles area  56, 28 , 192 degree.

To know more about Triangle

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8 0
2 years ago
Determine the discriminant of x2 = 4. <br><br> A. 17 <br> B. 16 <br> C. -15 <br> D. -10
tino4ka555 [31]
The discriminant is b<span>²-4ac
We can rewrite x</span>² = 4 to x<span>² + 0x - 4 = 0
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The answer is B
6 0
3 years ago
Read 2 more answers
Solve the inequality -d ≥ 0.5
Mariulka [41]

Answer:

d ≤ -0.5

Step-by-step explanation:

Multiply each term by -1

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Irina-Kira [14]

Answer: x≈0.732

Step-by-step explanation:

You need to find the value of the variable "x".

To solve for "x" you need to apply the following property of logarithms:

log(m)^n=nlog(m)

Apply logarithm on both sides of the equation:

90^x=27\\\\log(90)^x=log(27)

Now, applying the property mentioned before, you can rewrite the equation in this form:

xlog(90)=log(27)

Finally, you can apply the Division property of equality, which states that:  

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Therefore, you need to divide both sides of the equation by log(90). Finally, you get:

\frac{xlog(90)}{log(90)}=\frac{log(27)}{log(90)}\\\\x=\frac{log(27)}{log(90)}

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7 0
3 years ago
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Luda [366]

Answer:

B.

Step-by-step explanation:

Although the numbers given are negative, we can see that by the lines surrounding them, it is asking for their absolute value. Since absolute values are always positive, the correct answer would be B.

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