Answer:
Where
and 
Since the distribution for X is normal then the distribution for the sample mean is also normal and given by:



So then is appropiate use the normal distribution to find the probabilities for 
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". The letter
is used to denote the cumulative area for a b quantile on the normal standard distribution, or in other words: 
Solution to the problem
Let X the random variable that represent the variable of interest of a population, and for this case we know the distribution for X is given by:
Where
and 
Since the distribution for X is normal then the distribution for the sample mean
is also normal and given by:



So then is appropiate use the normal distribution to find the probabilities for 
Answer:
Step-by-step explanation:
a) -x-4(1-x) =
−
2
x
−4
(
1
−
x
)
.
2
x
−
4
b) 3(5x-2)-5(3-4x) =
3
⋅
(5
x
−
2
)
−
5
⋅
(
5
−
4
x
)
35
x − 31
c) √2(3-x)-2(1-x√2) =
√
2
x
⋅
(
3
−x
)
−
2
⋅(
1
−
x
√
2
)
.
2
x
√
2
+
3
√
2
x
-√
2
x
x
−
2
Sin 35 = x/15
x = sin 35*15
x = 8.6 cm
Answer: y= 3x-1
Step-by-step explanation:
Equation of a straight line:
y = mx + b ------(i)
Step by Step Solution:
Step 1: Calculating Slope (m).
m =
y2-y1
x2-x1
m =
2--1
1-0
m =
3
1
m = 3
Now putting value of m in equation (i)
y = 3x + b -----(ii)
Step 2: Calculating Y-intercept (b).
Lets choose the first point, (0,-1) for calculating y-intercept:
y = mx + b
-1 = 3(0) + b
-1 = 0 + b
-1 = b
b = -1
Answer:
Step-by-step explanation:
THANKS for the points