Answer: from up to down 9, from side to side 12
Answer:
(a) The average grade point is 2.5.
(b) The relative frequency table is show below.
(c) The mean of the relative frequency distribution is 0.3333.
Step-by-step explanation:
The given data set is
4, 4, 4, 3, 3, 3, 1, 1, 1, 1
(a)
The average grade point is



Therefore the average grade point is 2.5.
(b)

The relative frequency table is show below:
x f Relative frequency
4 3 
3 3
1 4 
(c)
Mean of the relative frequency distribution is


Therefore the mean of the relative frequency distribution is 0.3333.
Side 1 = short side = 2x-3
side 2 = longer side = (short side) + 6 = (2x-3)+6 = 2x+3
side 3 = side 2 = 2x+3
Side 2 and side 3 are the longer two congruent sides
Add up the three sides and set them equal to the given perimeter of 33. Solve for x
(side1)+(side2)+(side3) = perimeter
(2x-3)+(2x+3)+(2x+3) = 33
(2x+2x+2x) + (-3+3+3) = 33
6x+3 = 33
6x+3-3 = 33-3
6x = 30
6x/6 = 30/6
x = 5
If x = 5, then the longer sides are 2*x+3 = 2*5+3 = 10+3 = 13 inches each
(note: the short side is 2*x-3=2*5-3=10-3 = 7 inches)
Answer: 13 inches
Answer:
The standard deviation of weight for this species of cockroaches is 4.62.
Step-by-step explanation:
Given : A different species of cockroach has weights that are approximately Normally distributed with a mean of 50 grams. After measuring the weights of many of these cockroaches, a lab assistant reports that 14% of the cockroaches weigh more than 55 grams.
To find : What is the approximate standard deviation of weight for this species of cockroaches?
Solution :
We have given,
Mean 
The sample mean x=55
A lab assistant reports that 14% of the cockroaches weigh more than 55 grams.
i.e. P(X>55)=14%=0.14
The total probability needs to sum up to 1,



The z-score value of 0.86 using z-score table is z=1.08.
Applying z-score formula,

Where,
is standard deviation
Substitute the values,





The standard deviation of weight for this species of cockroaches is 4.62.