Answer:
[3.75 years, 5.45 years]
Step-by-step explanation:
The 90% confidence interval is given by the interval
![\large [\bar x-t^*\frac{s}{\sqrt n}, \bar x+t^*\frac{s}{\sqrt n}]](https://tex.z-dn.net/?f=%5Clarge%20%5B%5Cbar%20x-t%5E%2A%5Cfrac%7Bs%7D%7B%5Csqrt%20n%7D%2C%20%5Cbar%20x%2Bt%5E%2A%5Cfrac%7Bs%7D%7B%5Csqrt%20n%7D%5D)
where
<em>
is the sample mean </em>
<em>s is the sample standard deviation </em>
<em>n is the sample size
</em>
is the 0.05 (5%) both-sided (**) critical value for <em>the Student's t-distribution with 19 degrees of freedom (sample size -1), which is an approximation to the Normal distribution for small samples (n≤ 30).
</em>
Either by using a table or the computer, we find
and our 90% confidence interval is
![\large [4.6-1.729*\frac{2.2}{\sqrt{20}}, 4.6+1.729*\frac{2.2}{\sqrt{20}}]=\boxed{[3.75,5.45]}](https://tex.z-dn.net/?f=%5Clarge%20%5B4.6-1.729%2A%5Cfrac%7B2.2%7D%7B%5Csqrt%7B20%7D%7D%2C%204.6%2B1.729%2A%5Cfrac%7B2.2%7D%7B%5Csqrt%7B20%7D%7D%5D%3D%5Cboxed%7B%5B3.75%2C5.45%5D%7D)
(**) 5% of the area to the left of 
and 5% to right of for a total of 90% inside the interval ![\large [-t^*,+t^*]](https://tex.z-dn.net/?f=%5Clarge%20%5B-t%5E%2A%2C%2Bt%5E%2A%5D)
Answer:
Step-by-step explanation:
This is a binomial probability distribution because there re only 2 possible outcomes. It is either a surveyed company outsourced some part of their manufacturing process in the past two to three years. The probability of success, p would be that a randomly selected company x, outsourced some part of their manufacturing process in the past two to three years. From the information given, p = 54/100 = 0.54
Number of success, x = 338
Number of samples, n = 555
We want to determine the probability that 338 or more companies outsourced some part of their manufacturing process in the past two or three years which is expressed as
P(x ≥ 338)
From the binomial probability calculator,
P(x ≥ 338) = 0.0006
The percentage is 0.0006 × 100 = 0.06%
Answer:
690 ÷ 5 = 138
Step-by-step explanation:
They should save $138 each weak.
Answer:
$$$$4.17
Step-by-step explanation:
20-13.83=6,17
6.17-2=4.17
