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ruslelena [56]
3 years ago
8

Can someone please help me with this

Mathematics
1 answer:
Tresset [83]3 years ago
6 0

Answer:

Step-by-step explanation:

Answered by Gauthmath

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Suppose a sample of 100 families of four vacationing at Niagara Falls resulted in sample mean of $282.45 spent per day and a sam
Juli2301 [7.4K]

Given Information:

Mean = μ = $282.45

Standard deviation = σ = $64.50

Sample size = n = 100

Confidence level = 95%

Required Information:  

95% Confidence interval = ?

Answer:

95% Confidence interval = ($269.81, $295.09)

Step-by-step explanation:

We are given a Normal Distribution, which is a continuous probability distribution and is symmetrical around the mean. The shape of this distribution is like a bell curve and most of the data is clustered around the mean. The area under this bell shaped curve represents the probability.

What is Confidence Interval?

The confidence interval represents an interval that we can guarantee that the target variable will be within this interval for a given confidence level.  

The confidence interval is given by

CI = \bar{x} \pm MoE\\

Where \bar{x} is the mean and MoE is the margin of error given by

MoE = z_{\alpha/2}(\frac{\sigma}{\sqrt{n} } ) \\

Where σ is the standard deviation, n is the sample size and z_{\alpha/2} is the z-score corresponding to 95% confidence level.

z_{\alpha/2} = 1 - 0.95 = 0.05/2 = 0.025\\\\z_{0.025} = 1.96

MoE = 1.96\cdot \frac{64.50}{\sqrt{100} } \\\\MoE = 1.96\cdot 6.45\\\\MoE = 12.64\\

Finally, the confidence interval is

CI = \bar{x} \pm MoE\\\\CI = 282.45 \pm 12.64\\\\CI = 282.45 - 12.64 \: and \: 282.45 + 12.64\\\\CI = \$269.81 \: and \:\:\$295.09\\

Therefore, we are 95% sure that the true population mean amount spent per day by a family of four visiting Niagara Falls is within the interval of ($269.81, $295.09)

3 0
3 years ago
Which expression is a monomial?
creativ13 [48]
I need options but this is an example of a monomial:

(2x^2)
5 0
3 years ago
If a bus leaves every 8 minutes and a other bus leaves every 10 how often will both buses leave at the same time
olga nikolaevna [1]

Answer:

i think its 10:00am

Step-by-step explanation:

6 0
3 years ago
Help me on this plz and thank you
Ghella [55]

By solving for x you get x=6

3 0
2 years ago
Read 2 more answers
Which 2 numbers have a mean average of 10 and a range of 4
Aloiza [94]
Simply the answer is 12 and 8.

Mark brainliest please

Hope this helps you
5 0
3 years ago
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