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
Answer:
Step-by-step explanation:
B. The system has infinitely many solutions. The system has one solution.
Answer:
95+75=170 mph=speed at which the two trains are moving apart
travel time=distance/speed=374/170=2.2
How long will it take for the two trains to be 374 miles apart? 2.2 hrs
Step-by-step explanation:
Answer:
16 ft
Step-by-step explanation:
Let the width of the rectangle be x ft
Therefore, length = (x + 2) ft
Area of the rectangle = 15 square ft
X = larger number, y = smaller number
x = 5y
x - y = 36
5y - y = 36
4y = 36
y = 36/4
y = 9
x = 5y
x = 5(9)
x = 45
ur numbers are 45 and 9 <==
