Answer:
P(2.50 < Xbar < 2.66) = 0.046
Step-by-step explanation:
We are given that Population Mean, 
= 2.58 and Standard deviation, 
= 0.75
Also, a random sample (n) of 110 households is taken.
Let Xbar = sample mean household size
The z score probability distribution for sample mean is give by;
Z = 
~ N(0,1)
So, probability that the sample mean household size is between 2.50 and 2.66 people = P(2.50 < Xbar < 2.66)
P(2.50 < Xbar < 2.66) = P(Xbar < 2.66) - P(Xbar 
2.50)
P(Xbar < 2.66) = P( < 
) = P(Z < -1.68) = 1 - P(Z 1.68)
= 1 - 0.95352 = 0.04648
P(Xbar 2.50) = P( 
) = P(Z -3.92) = 1 - P(Z < 3.92)
= 1 - 0.99996 = 0.00004
Therefore, P(2.50 < Xbar < 2.66) = 0.04648 - 0.00004 = 0.046
Answer:
12 cups
Step-by-step explanation:
If the size of the bag decreased by 20%, so will the number of cups held.
Number of cups held before the change = 15 cups
If the number of cups held after the 20% reduction in the size of the bag
= (100 - 20)% × 15
=80% × 15
= 12 cups
The new bags will hold 12 cups.
The vertex form is 
Step-by-step explanation:
The given equation 
is a parabola. The vertex of the parabola is of the form 
The parameters of the parabola are 
and 
The vertex of the x-coordinate is given by 
Thus, substituting the values of a and b in , we get,
Now, substituting 
in , we get,
Thus, the vertex is 
The equation of parabola to be in vertex form is 
where a is the coefficient of 
, h is vertex of the x-coordinate and k is the vertex of the y-coordinate.
Hence, 
and 
Thus, substituting the values in the equation of the vertex form,
Hence, the vertex form is
