Answer:
a)0.099834
b) 0
Step-by-step explanation:
To solve for this question we would be using , z.score formula.
The formula for calculating a z-score is is z = (x-μ)/σ, where x is the raw score, μ is the population mean, and σ is the population standard deviation.
A candy maker produces mints that have a label weight of 20.4 grams. Assume that the distribution of the weights of these mints is normal with mean 21.37 and variance 0.16.
a) Find the probability that the weight of a single mint selected at random from the production line is less than 20.857 grams.
Standard Deviation = √variance
= √0.16 = 0.4
Standard deviation = 0.4
Mean = 21.37
x = 20.857
z = (x-μ)/σ
z = 20.857 - 21.37/0.4
z = -1.2825
P-value from Z-Table:
P(x<20.857) = 0.099834
b) During a shift, a sample of 100 mints is selected at random and weighed. Approximate the probability that in the selected sample there are at most 5 mints that weigh less than 20.857 grams.
z score formula used = (x-μ)/σ/√n
x = 20.857
Standard deviation = 0.4
Mean = 21.37
n = 100
z = 20.857 - 21.37/0.4/√100
= 20.857 - 21.37/ 0.4/10
= 20.857 - 21.37/ 0.04
= -12.825
P-value from Z-Table:
P(x<20.857) = 0
c) Find the approximate probability that the sample mean of the 100 mints selected is greater than 21.31 and less than 21.39.
Answer: 3 liters for 1.89.
Step-by-step explanation:
1.89/3 = 0.63 per liter
6.90/ 10 = 0.69 per liter
Answer:
Step-by-step explanation:
The formula of an area of a kite:
d₁, d₂ - diagonals
We have A = 120 cm² and d₁ = 16 cm. Substitute:
<em>divide both sides by 8</em>
The standard eqn of a parabola in vertex form is y-k = a(x-h)^2, where (h,k) is the vertex. There are a good number of steps involved. I don't think it wise not to "show work." I cannot answer this question without going through all those steps.
However, there's an easier way to find the vertex. Identify the coefficients a, b and c:
a= -4, b= -3 and c = 1
Then the x-coord. of the vertex is x = -b / (2a). Subst. -3 for b and -4 for a and simplify. x = ??
Then find the y-coord. of the vertex by subbing your result, above, into the original equation.
Write the vertex as (h,k).
Once you have this vertex, you can find the equation in vertex form as follows:
Start with the general form y-k = a(x-h)^2, where (h,k) is the vertex.
You've already found the vertex (h,k). Subst. h and k into the general form, above. Then only the coefficient "a" remains undefined.
You solve this by plugging one equation into the other. Usually you have to rewrite one equation to make this work. In this case I choose to rewrite y-4x=0 as y=4x.
After plugging it into the second, you get:
3x + 6*4x = 9 => 27x = 9 => x=1/3
Putting this solution back into y=4x gives us y=4/3
