The scores on a test are normally distributed with a mean of 110 and a standard deviation of 22. What is the score that is 3 sta
1 answer:
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The 85th percentile is the cutoff time 
such that
In other words, the 85th percentile refers to the time needed to belong to the top 15% of the distribution; more generally, the
percentile is the top 
of the distribution.
Anyway, to find this value of, transform 
to a random variable 
with the standard normal distribution using
where
is the mean of and 
is the standard deviation of .
Here
is used to denote the z-score corresponding to the cutoff time . Referring to a z-score table, you find that this occurs for 
. So,
In other words, the 85th percentile refers to the time needed to belong to the top 15% of the distribution; more generally, the
Anyway, to find this value of
where
Here
Answer:
a) 4u + 2v = (8, 12, 14)
b) 2u - v = (0, 6, 1)
c) |u + 4v| = 16.9
Step-by-step explanation:
When we add/subtract vectors, we add/subtract their components. For example
a = (a1,a2,a3)
b = (b1,b2,b3)
a+b = (a1 + b1, a2 + b2, a3 + b3)
|a| is the modulus of vector a, given by
In this problem, we have that:
u = (1,3,2)
v = (2,0,3)
(a) 4u+2v
4u = 4(1,3,2) = (4,12,8)
2v = 2(2,0,3) = (4,0,6)
4u + 2v = (8, 12, 14)
(b) 2u-v
2u = 2(1,3,2) = (2,6,4)
v = (2,0,3)
2u - v = (0, 6, 1)
(c) |u + 4v|
u = (1,3,2)
4v = 4(2,0,3) = (8,0,12)
u + 4v = (9,3,14)