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jljhenkel
16.10.2020 •
Mathematics
2.
The heights of horses who compete in the Melbourne Derby are
normally distributed with a mean of 66 inches and a standard
deviation of 3 inches.
(a) If a horse is randomly selected from this race, what height
would you expect it to be?
(b) What percentage of horses who compete in the Melbourne
Derby have heights between 60 and 72 inches?
(c) In a particular year there are 25 horses running in the
Melbourne Derby. How many of these would you expect
to have a height of less than 63 inches?
Solved
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Ответ:
66 inches ;
95.44 ;
4
Step-by-step explanation:
Given that:
Normal distribution with;
Mean(m) = 66 inches
Standard deviation (s) = 3 inches
A.) If a horse is chosen at random, Expected height will be equal to the mean of the distribution = 66 inches
B.) percentage horses who are between 60 and 72 inches
Zscore = ( x - m) / s
x = 60
Zscore = (60 - 66) / 3
Zscore = - 6/3
= - 2
P(Z < - 2) = 0.0228
Zscore = ( x - m) / s
x = 72
Zscore = (72 - 66) / 3
Zscore = 6/3
= 2
P(Z < 2). = 0.9772
Between 60 and 72
0.9772 - 0.0228 = 95.44
c) In a particular year there are 25 horses running in the Melbourne Derby. How many of these would you expect to have a height of less than 63 inches?
Zscore = ( x - m) / s
x = 63
Zscore = (63 - 66) / 3
Zscore = - 3/3
= - 1
P(Z < - 1) = 0.1587
0.1587 * 25 = 3. 967 = 4
Ответ:
Area =
.
Step-by-step explanation:
Given : Vanessa uses the expressions (3x² + 5x + 10) and (x² – 3x – 1) to represent the length and width of her patio.
To find : Which expression represents the area (lw) of Vanessa’s patio?
Solution : We have given
Length = (3x² + 5x + 10)
Width = (x² – 3x – 1)
Area= length * width .
Area = (3x² + 5x + 10) * (x² – 3x – 1).
Area = 3x² (x² – 3x – 1) + 5x (x² – 3x – 1) + 10 (x² – 3x – 1).
Area =
.
Combine like terms
Area =
.
Area =
.
Area =
.
Therefore, Area =
.