There are 50 cars on display at a car show. Of these,18 were manufactured before 1945. What percent of the cars were manufacture
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Answer:
The confidence interval for the mean is given by the following formula:
(1)
And for this case the 95% confidence interval is given by (2.13; 2.37)
We have a point of estimate for the sample mean with this formula:
And for the margin of error we have the following estimation:
Step-by-step explanation:
Previous concepts
A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".
The margin of error is the range of values below and above the sample statistic in a confidence interval.
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
represent the sample mean
population mean (variable of interest)
s represent the sample standard deviation
n represent the sample size
Solution to the problem
The confidence interval for the mean is given by the following formula:
(1)
And for this case the 95% confidence interval is given by (2.13; 2.37)
We have a point of estimate for the sample mean with this formula:
And for the margin of error we have the following estimation:
Answer:
Decimal 0.333 to a fraction in simplest form is:
Step-by-step explanation:
Given the decimal
Multiply and divide by 10 for every number after the decimal point.
There are three digits to the right of the decimal point, therefore multiply and divide by 1000.
Thus,
∵ 0.333×1000 = 333
Let us check if we can reduce the fraction
For this, we need to find a common factor of 333 and 1000 in order to cancel it out.
But, first, we need to find the Greatest Common Divisor (GCD) of 333, 1000
<u>Greatest Common Divisor (GCD) : </u>
The GCD of a, b is the largest positive number that divides both a and b without a remainder.
Prime Factorization of 333: 3 · 3 · 37
Prime Factorization of 1000: 2 · 2 · 2 · 5 · 5 · 5
As there is no common factor for 333 and 1000, therefore, the GCD is 1.
Important Tip:
- As GCD is 1, therefore the fraction can not be simplified.
Therefore, decimal 0.333 to a fraction in simplest form is: