Answer
given,
mean = 12 Kg
standard deviation = 0.5 Kg
assume the observed statistic is = 11.1
now,
assuming the number of sample = 4
n = 4
Hypothesis test:
H₀ : μ≥ 12
Ha : μ < 12
now,
significant level α = 0.05
z* = -3.60
Test statistics, Z* = -3.60
P-value
P(Z<-3.60) = 0.002 (from z- table)
P- value = 0.002
now,
reject the value of H₀ when P-value < α
0.002 < 0.05
since, it is less P-value < α , we have to reject the null hypothesis
The mean is and standard deviation is
. Then the variable
.
Use substitution , then the variable
.
The probability can be calculated in the following way:
for X=80, and
. From the diagram
.
Conclusion: if 188 students take the exam, then 188·0.84=157.92 (157) would receive a score above 80
Answer:
Step-by-step explanation:
Vertex A of the triangle ABC when rotated by 90° counterclockwise about the origin,
Rule to be followed,
A(x, y) → P(-y, x)
Therefore, A(1, 1) → P(-1, 1)
Similarly, B(3, 2) → Q(-2, 3)
C(2, 5) → R(-5, 2)
Triangle given in second quadrant will be the triangle PQR.
If the point P of triangle PQR is reflected across a line y = x,
Rule to be followed,
P(x, y) → X(y, x)
P(-1, 1) → X(1, -1)
Similarly, Q(-2, 3) → Y(3, -2)
R(-5, 2) → Z(2, -5)
Therefore, triangle given in fourth quadrant is triangle XYZ.
