Answer:
And we can use the complement rule and we got:
Step-by-step explanation:
Previous concepts
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".
The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".
Solution to the problem
Let X the random variable that represent the bank account balances of a population, and for this case we know the distribution for X is given by:
Where and
Since the distribution of X is normal then the distribution for the sample mean is given by:
And we can use the z score formula given by:
And using this formula we got:
And we can use the complement rule and we got:
(4,h)
(5,h)
(6,h) N(s)=6*2=12 n(a)=3 p(a)=0.25
Answer:
a) 0.62%
b) 518 g
Step-by-step explanation:
a)
Here we want the area under the Normal curve of mean = 500 g and standard deviation s = 10 g to the left of 475 (the probability that the machine produces a box with less than 475 g of cereal).
With the help of a spreadsheet we found that value is 0.0062 or 0.62% (another way of seeing it is that 62 boxes out of 10,000 will have 475 g or less)
<h3>See picture</h3>
b)
Here we want to find a value of such that the area of the Normal curve of mean and standard deviation 10 to the left of 500 is 4% or 0.04
If we make the change
then this is equivalent to finding a value of z for which the area under the Normal curve N(0,1) (mean = 0 s = 1) to the left of z is 4% = 0.04
Either by using a table or spreadsheet, we find that value is z = -1.751
So,
and the manufacturer must set its filling machine to the target weight of 518 g.
8 is the common factor
24÷8=3
48÷8=6
144÷8=18
4n + 2n = 4
6n = 4
Divide by 6 both sides
n = 2/3