Answer:
The proportion of children that have an index of at least 110 is 0.0478.
Step-by-step explanation:
The given distribution has a mean of 90 and a standard deviation of 12.
Therefore mean,
= 90 and standard deviation,
= 12.
It is given to find the proportion of children having an index of at least 110.
We can take the variable to be analysed to be x = 110.
Therefore we have to find p(x < 110), which is left tailed.
Using the formula for z which is p( Z <
) we get p(Z <
= 1.67).
So we have to find p(Z ≥ 1.67) = 1 - p(Z < 1.67)
Using the Z - table we can calculate p(Z < 1.67) = 0.9522.
Therefore p(Z ≥ 1.67) = 1 - 0.9522 = 0.0478
Therefore the proportion of children that have an index of at least 110 is 0.0478
If the total value of the coins is $15. The number of each type of coin is: 31 quarters, 72 dimes.
<h3>Number of each type of coin</h3>
Let D = number of dimes
Let Q = the number of quarters
Equations
d + q = 103
0.10d + 0.25q = 15
d = 103 -q
0.10(103 -q) + 0.25q = 15
10.3 - 0.10q + 0.25q = 15
0.15q = 4.7
q=4.7/0.15
q=31 quarters
Substitute q into second equation
D+31=103
D=72 dimes
Therefore the number of each type of coin is: 31 quarters, 72 dimes.
Learn more number of each coin here:brainly.com/question/13934075
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Step-by-step explanation:
diameter: 8
radius: 4
height: 18
![A=2\pi rh+2\pi r^2\\A=2\pi(4)(18)+2\pi(4)^2\\A=2\pi(72)+2\pi(16)\\A=144\pi+32\pi\\A=176\pi](https://tex.z-dn.net/?f=A%3D2%5Cpi%20rh%2B2%5Cpi%20r%5E2%5C%5CA%3D2%5Cpi%284%29%2818%29%2B2%5Cpi%284%29%5E2%5C%5CA%3D2%5Cpi%2872%29%2B2%5Cpi%2816%29%5C%5CA%3D144%5Cpi%2B32%5Cpi%5C%5CA%3D176%5Cpi)