Number 1 might be A and number 2 might be B. I'm not sure though.
Answer: a) α = 0.7927, b) at u=14.8, β = 0.99767, at u = 14.9, β= 0.2073
Step-by-step explanation: a) from the question, u= population mean = 15 and x= sample mean = 14.9
σ = population standard deviation = 0.5, n = sample size = 50.
We get the probability of committing a type 1 error by using the z score.
Z = x - u/(σ/√n)
Z = 14.9 - 15/(0.5/√50)
Z = - 0.1/0.0707
Z = - 1.41.
By checking the the probabilistic value attached to this z score using a standard normal distribution table whose area is to the left of the distribution, we have that
P(z=-1.41) = 0.7927.
Hence the probability of committing a type 1 error is 0.7927
b)
at x = 14.8 ( I let ua=x=14.8)
Z = x - u/(σ/√n)
Z = 14.8 - 15/(0.5/√50)
Z = - 0.2/ 0.0707
Z = - 2.83
Using the standard normal distribution table, we have that
P(z=-2.38) = 0.00233.
But α + β = 1
Where α= probability of committing a type 1 error
β = probability of committing a type 2 error.
β = 1 - α
β = 1 - 0.00233
β = 0.99767
At x = 14.9
Z = x - u/(σ/√n)
Z = 14.9 - 15/(0.5/√50)
Z = - 0.1/0.0707
Z = - 1.41.
P(z=-1.41) = 0.7927.
α = 0.7927.
But α + β = 1
β = 1 - 0.7927
β = 0.2073
Answer:
Segment JK is a chord in circle H
Line LM is a secant to circle H
Step-by-step explanation:
* Lets revise some definition in the circle
- The radius of the circle is a line segment drawn from the center of
the circle to a point on the circumference of the circle
- The chord of a circle is a line segment whose endpoints lie on the
circumference of the circle
- The secant is a line intersect the circle in two points
- The tangent is a line touch or intersect the circle in one point
* Now lets solve the problem
- In circle H
∵ JK is a segment in circle H
∵ Point J lies on the circumference of circle H
∵ Point K lies on the circumference of circle H
∴ Segment JK is a chord in circle H
∵ LM is a line
∵ LM intersect circle H in two points L and M
∴ Line LM is a secant to circle H
