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sasho [114]
2 years ago
14

1. You go to a restaurant and your bill is $24,00. You are going to tip 16%

Mathematics
2 answers:
aev [14]2 years ago
7 0

Answer: #1. $3.84     #2. $2.30

Step-by-step explanation:

24.00 x .16=3.84

23 x .10=2.30

myrzilka [38]2 years ago
4 0

Answer:

1. $3.84

2. $2. 30

Step-by-step explanation:

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a) The 98% confidence interval for the mean weight is between 10.00409 grams and 10.00471 grams

b) 49 measurements are needed.

Step-by-step explanation:

Question a:

We have that to find our \alpha level, that is the subtraction of 1 by the confidence interval divided by 2. So:

\alpha = \frac{1 - 0.98}{2} = 0.01

Now, we have to find z in the Ztable as such z has a pvalue of 1 - \alpha.

That is z with a pvalue of 1 - 0.01 = 0.99, so Z = 2.327.

Now, find the margin of error M as such

M = z\frac{\sigma}{\sqrt{n}}

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M = 2.327\frac{0.0003}{\sqrt{5}} = 0.00031

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The upper end of the interval is the sample mean added to M. So it is 10 + 0.00031 = 10.00471 grams

The 98% confidence interval for the mean weight is between 10.00409 grams and 10.00471 grams.

(b) How many measurements must be averaged to get a margin of error of +/- 0.0001 with 98% confidence?

We have to find n for which M = 0.0001. So

M = z\frac{\sigma}{\sqrt{n}}

0.0001 = 2.327\frac{0.0003}{\sqrt{n}}

0.0001\sqrt{n} = 2.327*0.0003

\sqrt{n} = \frac{2.327*0.0003}{0.0001}

(\sqrt{n})^2 = (\frac{2.327*0.0003}{0.0001})^2

n = 48.73

Rounding up

49 measurements are needed.

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