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
Combine like terms to get -4x^2-2x
9514 1404 393
Answer:
yes, about 2.05 inches
Step-by-step explanation:
The Pythagorean theorem can be used to find the width of the TV.
w^2 +h^2 = d^2
w = √(d^2 -h^2)
w = √(42^2 -18^2) = √1440 = 12√10
w ≈ 37.95 . . . inches
This dimension is less than 40 inches by a margin of ...
40 -37.95 = 2.05 . . . inches
The TV will fit, with 2.05 inches of space remaining.
