Given the total number of students are 180, the mean of data is 88g, and standard deviation is 1g.
A normal curve is a bell-shaped curve with symmetry about the mean and it spreads uniformly on both sides (left side and right side) of the mean.
The empirical rule is also called "68-95-99.7" rule. It says that :-
A) 68% of the data values fall between 1 standard deviation about mean (34% on left side and 34% on right side),
B) 95% of the data values fall between 2 standard deviations about mean (47.5% on left side and 47.5% on right side), and
C) 99.7% of the data values fall between 3 standard deviations about mean (49.85% on left side and 49.85% on right side).
According to distribution of normal curve and "68-95-99.7" empirical rule, we can say 49.85% of data values are above the mean within 3 standard deviations.
So it means 49.85% of total students report readings more than 88g.
Number of students reporting readings more than 88g = 49.85% of 180 = 0.4985 × 180 = 89.73
Hence, approximately 89 students report readings more than mean value.
Answer:
f−1(y)=4(y−7) is the inverse function
9x-3 +(3-5x)=5x-15+(3-5x)
4x=18
x=18/4
x=9/2
Answer:
a = - 2, b = - 6
Step-by-step explanation:
Substitute the values of the zeros into the polynomial and equate to zero.
x² +(a + 1)x + b
x = - 2 → (- 2)² - 2(a + 1) + b = 0 , that is
4 - 2a - 2 + b = 0
2 - 2a + b = 0 ( subtract 2 from both sides )
- 2a + b = - 2 → (1)
x = 3 → 3² + 3(a + 1) + b = 0, that is
9 + 3a + 3 + b = 0
12 + 3a + b = 0 ( subtract 12 from both sides )
3a + b = - 12 → (2)
Subtract (1) from (2) term by term to eliminate b
5a = - 10 ( divide both sides by 5 )
a = - 2
Substitute a = - 2 into either of the 2 equations and evaluate for b
Substituting into (2)
3(- 2) + b = - 12
- 6 + b = - 12 ( add 6 to both sides )
b = - 6
Thus a = - 2 and b = - 6
