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natka813 [3]
4 years ago
13

In a survey, 16 people were asked how much they spent on their child's last birthday gift. The results were roughly bell-shaped

with a mean of $37 and standard deviation of $17. Construct a confidence interval at a 95% confidence level.
Mathematics
1 answer:
Ludmilka [50]4 years ago
6 0

Answer:

CI= [28.67,45.33]

Step-by-step explanation:

-Given the mean is $37 and the standard deviation is $17

#A 95% confidence interval can be calculated as follows:

CI=\mu\pm z \frac{\sigma}{\sqrt{n}}\\\\=\mu\pm z_{0.025}\frac{\sigma}{\sqrt{n}}\\\\=37\pm1.96\times\frac{17}{\sqrt{16}}\\\\\\=37\pm8.33\\\\=[28.67,\ 45.33]

Hence, the 95% confidence interval is [28.67,45.33]

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Blababa [14]

Answer:

The probability is 1/2 or 50%

Step-by-step explanation:

P(roll less than 4) = Probability of rolling less than 4

There are 3 numbers that are less than 4.

1, 2, 3, 4, 5, 6.

There is a total of 6 sides.

So,

3/6 simplified to 1/2 or 50%

6 0
3 years ago
Explain why 1/2 ab sin(theta) gives the area of a triangle with sides a and ???? and included angle theta.
Jet001 [13]

Answer:

Please find the attachment.

Step-by-step explanation:

We are asked to explain why \frac{1}{2}ab\cdot \text{sin}(\theta) gives the area of a triangle with sides a and b and included angle theta.    

We know that area of a triangle is equal to half the product of base and height of the triangle.

\text{Area of triangle}=\frac{1}{2}\cdot bh

Upon looking at our given triangle, we can see that the base of the triangle is equal to 'a'.

The height of the triangle can be determined using sin(theta) as sine relates opposite side of right triangle with its hypotenuse.

\text{sin}=\frac{\text{Opposite}}{\text{Hypotenuse}}

\text{sin}(\theta)=\frac{h}{b}    

h=b\cdot \text{sin}(\theta)  

Upon substituting our given values in area formula, we will get:

\text{Area of triangle}=ab\cdot \text{sin}(\theta)  

Hence, proved.

8 0
3 years ago
Vector u has its initial point at (17, 5) and its terminal point at (9, -12). Vector v has its initial point at (12, 4) and its
Ratling [72]

\bf \vec{u}~~ \begin{cases} (17,5)\\ (9,12) \end{cases}\implies \implies \stackrel{\textit{component form}}{} \\\\\\ \vec{v}~~ \begin{cases} (12,4)\\ (3,-2) \end{cases}\implies \implies \stackrel{\textit{component form}}{} \\\\[-0.35em] ~\dotfill

\bf 3\vec{u}\implies 3\implies  \\\\\\ 2\vec{v}\implies 2\implies  \\\\\\ 3\vec{u}-2\vec{v}\implies -\implies + \\\\\\ \implies  \\\\[-0.35em] ~\dotfill\\\\ ||3\vec{u}-2\vec{v}||\implies ||||\implies \sqrt{(-16)^2+33^2} \\\\\\ \sqrt{1345}\implies 36.67

3 0
3 years ago
Find the area of a circle with radius 7 yd.
Vladimir79 [104]

Answer:

153.86 yd²

Step-by-step explanation:

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4 years ago
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