Respuesta :
The margin of error is 3.71 and confidence interval is (350.04,361.46).
What is normal distribution?
This same probability density function for just a continuous random variable inside a system defines the Normal Distribution. Let's assume that X is the random variable and that f(x) is the probability density function. In order to determine the probability of the random variable X, it defines a function that is integrated between both the range as well as interval (x to x + dx) while taking into account values among x and x+dx.
f(x) ≥ 0 ∀ x ϵ (−∞,+∞)
And -∞∫+∞ f(x) = 1
What is margin of error?
The level of error in results from surveys using random sampling is known as the margin of error. A higher error margin in statistics denotes a lower likelihood of relying on a survey's or poll's findings, meaning that there will be less confidence in the results' ability to accurately represent a population.
Given,
Sample size = 400
Mean = $357.75
Standard deviation = $37.89
At 95% confidence level, z = 1.96
We first find the margin of error.
Margin of error is given by
z ×σ/[tex]\sqrt{n}[/tex]
= 1.96 ×37.89/20
=3.71.
95% confidence interval would be
x ± margin of error
= 375.75 ± 3.71
= (350.04,361.46)
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