Let's call our estimate x. It will be the average of n IQ scores. Our average won't usually exactly equal the mean 97. But if we repeated averages over different sets of tests, the mean of our estimate the average would be the same as the mean of a single test,
μ = 97
Variances add, so the standard deviations add in quadrature, like the Pythagorean Theorem in n dimensions. This means the standard deviation of the average x is
σ = 17/√n
We want to be 95% certain
97 - 5 ≤ x ≤ 97 + 5
By the 68-95-99.7 rule, 95% certain means within two standard deviations. That means we're 95% sure that
μ - 2σ ≤ x ≤ μ + 2σ
Comparing to what we want, that's means we have to solve
2σ = 5
2 (17/√n) = 5
√n = 2 (17/5)
n = (34/5)² = 46.24
We better round up.
Answer: We need a sample size of 47 to be 95% certain of being within 5 points of the mean
27/8 = 3 3/8
3 whole pizzas were left
5/8 is left over because 8/8 - 3/8 = 5/8
Answer: No they are not. The first one is 54 and the second one is 51.
Step-by-step explanation:
Answer:
See a solution process below:
Explanation:
Let's call the number of miles driven we are looking for
m
.
The the total cost of ownership for the first car model is:
12000
+
0.1
m
The the total cost of ownership for the second car model is:
14000
+
0.08
m
We can equate these two expressions and solve for
m
to find after how many miles the total cost of ownership is the same:
12000
+
0.1
m
=
14000
+
0.08
m
Next, we can subtract
12000
and
0.08
m
from each side of the equation to isolate the
m
term while keeping the equation balanced:
−
12000
+
12000
+
0.1
m
−
0.08
m
=
−
12000
+
14000
+
0.08
m
−
0.08
m
0
+
(
0.1
−
0.08
)
m
=
2000
+
0
0.02
m
=
2000
Now, we can divide each side of the equation by
0.02
to solve for
m
while keeping the equation balanced:
0.02
m
0.02
=
2000
0.02
0.02
m
0.02
=
100000
After 100,000 miles the total cost of ownership of the two cars would be the same.
