if a company has 5 employees with annual saleries of $40,000, $50,000, $40,000, $60,000 and $90,000 what is the mean anulal sala
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Given:
The bases of a trapezoid lie on the lines
To find:
The equation that contains the midsegment of the trapezoid.
Solution:
The slope intercept form of a line is
Where, m is slope and b is y-intercept.
On comparing with slope intercept form, we get
On comparing with slope intercept form, we get
The slope of parallel lines are equal and midsegment of a trapezoid is parallel to the bases. So, the slope of the bases line and the midsegment line are equal.
The y-intercept of one base is 7 and y-intercept of second base is -5. The y-intercept of the midsegment is equal to the average of y-intersects of the bases.
So, the y-intercept of the required line is 1.
Putting m=2 and b=1 in slope intercept form, we get
Therefore, the equation of line that contains the midsegment of the trapezoid is .
Question 1
probability between 2.8 and 3.3
The graph of the normal distribution is shown in the diagram below. We first need to standardise the value of X=2.8 and value X=3.3. Standardising X is just another word for finding z-score
z-score for X = 2.8
(the negative answer shows the position of X = 2.8 on the left of mean which has z-score of 0)
z-score for X = 3.3
The probability of the value between z=-0.73 and z=0.49 is given by
P(Z<0.49) - P(Z<-0.73)
P(Z<0.49) = 0.9879
P(Z< -0.73) = 0.2327 (if you only have z-table that read to the left of positive value z, read the value of Z<0.73 then subtract answer from one)
A screenshot of z-table that allows reading of negative value is shown on the second diagram
P(Z<0.49) - P(Z<-0.73) = 0.9879 - 0.2327 = 0.7552 = 75.52%
Question 2
Probability between X=2.11 and X=3.5
z-score for X=2.11
z-score for X=3.5
the probability of P(Z<-2.41) < z < P(Z<0.98) is given by
P(Z<0.98) - P(Z<-2.41) = 0.8365 - 0.0080 = 0.8285 = 82.85%
Question 3
Probability less than X=2.96
z-score of X=2.96
P(Z<-0.34) = 0.3669 = 36.69%
Question 4
Probability more than X=3.4
P(Z>0.73) = 1 - P(Z<0.73) = 1-0.7673=0.2327 = 23.27%
probability between 2.8 and 3.3
The graph of the normal distribution is shown in the diagram below. We first need to standardise the value of X=2.8 and value X=3.3. Standardising X is just another word for finding z-score
z-score for X = 2.8
z-score for X = 3.3
The probability of the value between z=-0.73 and z=0.49 is given by
P(Z<0.49) - P(Z<-0.73)
P(Z<0.49) = 0.9879
P(Z< -0.73) = 0.2327 (if you only have z-table that read to the left of positive value z, read the value of Z<0.73 then subtract answer from one)
A screenshot of z-table that allows reading of negative value is shown on the second diagram
P(Z<0.49) - P(Z<-0.73) = 0.9879 - 0.2327 = 0.7552 = 75.52%
Question 2
Probability between X=2.11 and X=3.5
z-score for X=2.11
z-score for X=3.5
the probability of P(Z<-2.41) < z < P(Z<0.98) is given by
P(Z<0.98) - P(Z<-2.41) = 0.8365 - 0.0080 = 0.8285 = 82.85%
Question 3
Probability less than X=2.96
z-score of X=2.96
P(Z<-0.34) = 0.3669 = 36.69%
Question 4
Probability more than X=3.4
P(Z>0.73) = 1 - P(Z<0.73) = 1-0.7673=0.2327 = 23.27%