Answer:
Mean = 78.2
Standard deviation = 5.8
Step-by-step explanation:
Mathematically z-score;
= (x-mean)/SD
From the question;
12% of test scores were above 85
Thus;
P( x > 85) = 12%
P(x > 85) = 0.12
Now let’s get the z-score that has a probability of 0.12
This can be obtained from the standard normal distribution table and it is = 1.175
Thus;
1.175 = (85 - mean)/SD
let’s call the mean a and the SD b
1.175 = (85-a)/b
1.175b = 85 - a
a = 85 - 1.175b ••••••••(i)
Secondly 8% of scores were below 70
Let’s find the z-score corresponding to this proportion;
We use the standard normal distribution table as usual;
P( x < 70) = 0.08
z-score = -1.405
Thus;
-1.405 =( 70-a)/b
-1.405b = 70-a
a = 70 + 1.405b ••••••(ii)
Equate the two a
70 + 1.405b = 85 - 1.175b
85 -70 = 1.405b + 1.175b
15 = 2.58b
b = 15/2.58
b = 5.81
a = 70 + 1.405b
a = 70 + 1.405(5.81)
a = 78.16
So mean = 78.2 and Standard deviation is 5.8
The answer is yes. I think that I’m right
<span>For it to be finite, it must have an upper and lower bound. It has a lower bound...but what is the highest odd number greater than 27
There's no restriction; odd numbers go on forever.</span>
Answer:
(a)
(b)
(c)
Step-by-step explanation:
We are required to construct 3 linear equations starting with the given solution z = 1/3.
<u>Equation 1</u>
<u />
<u />
Multiply both sides by 9

Rewrite 3 as 5-2
9z=5-2
Add 2 to both sides
Our first equation is: 
<u>Equation 2</u>
<u />
<u />
Multiply both sides by 21

Rewrite 7 as 11-4
21z=11-4
Subtract 11 from both sides
Our second equation is: 
<u>Equation 3</u>
<u />
<u />
Multiply both sides by 6

Rewrite 6z as 4z+2z
4z+2z=2
Subtract 2z from both sides
Our third equation is: 
Answer:
slope of EF=
∠QSR=45°,
∠PTQ=90°
if RT=24
then SQ=48
square is always a rectangle
∠SUT=21°
Step-by-step explanation:
two line are perpendicular to each other if product of their slope equal to -1
=-1
slope of HE=
=-
slope of EF=
slope of EF=-1
=
slope of EF=
answer
∠QSR=45°,
∠PTQ=90°
if RT=24
then SQ=48
square is always a rectangle
given ∠SUT=3x+6
∠RUS=5x-4
∠SUT=∠RUS
3x+6=5x-4
x=5
∠SUT=3x+6=15+6=21°
∠SUT=21°