Step-by-step explanation:
-5(4a) = (-5a)4
(By commutative property of multiplication)
If inspection department wants to estimate the mean amount with 95% confidence level with standard deviation 0.05 then it needed a sample size of 97.
Given 95% confidence level, standard deviation=0.05.
We know that margin of error is the range of values below and above the sample statistic in a confidence interval.
We assume that the values follow normal distribution. Normal distribution is a probability that is symmetric about the mean showing the data near the mean are more frequent in occurence than data far from mean.
We know that margin of error for a confidence interval is given by:
Me=
α=1-0.95=0.05
α/2=0.025
z with α/2=1.96 (using normal distribution table)
Solving for n using formula of margin of error.

n=
=96.4
By rounding off we will get 97.
Hence the sample size required will be 97.
Learn more about standard deviation at brainly.com/question/475676
#SPJ4
The given question is incomplete and the full question is as under:
If the inspection division of a county weights and measures department wants to estimate the mean amount of soft drink fill in 2 liters bottles to within (0.01 liter with 95% confidence and also assumes that standard deviation is 0.05 liter. What is the sample size needed?
(3x + 4)2 = 14
(3x + 4)2 means that 2 will multiply both 3x and 4
2 * 3x = 6x 2 * 4 = 8
6x + 8 = 14
Move +8 to the other side of the equation
6x = 14 - 8 Note : Moving +8 to the other side will change the sign in front of it, that is from + to -
6x = 14 - 8
6x = 6
Divide both sides by 6 because of the 6 beside the x : 6x
6x/6 = 6/6
x = 1