How do I solve this?: The times of all 15 year olds who run a certain race are approximately normally distributed with a given m
ean = 18 sec and standard deviation = 1.2 sec. What percentage of the runners have times less than 14.4 sec?
2 answers:
We need to 'standardise' the value of X = 14.4 by first calculating the z-score then look up on the z-table for the p-value (which is the probability)
The formula for z-score:
z = (X-μ) ÷ σ
Where
X = 14.4
μ = the average mean = 18
σ = the standard deviation = 1.2
Substitute these value into the formula
z-score = (14.4 - 18) ÷ 1..2 = -3
We are looking to find P(Z < -3)
The table attached conveniently gives us the value of P(Z < -3) but if you only have the table that read p-value to the left of positive z, then the trick is to do:
1 - P(Z<3)
From the table
P(Z < -3) = 0.0013
The probability of the runners have times less than 14.4 secs is 0.0013 = 0.13%
The formula for z-score:
z = (X-μ) ÷ σ
Where
X = 14.4
μ = the average mean = 18
σ = the standard deviation = 1.2
Substitute these value into the formula
z-score = (14.4 - 18) ÷ 1..2 = -3
We are looking to find P(Z < -3)
The table attached conveniently gives us the value of P(Z < -3) but if you only have the table that read p-value to the left of positive z, then the trick is to do:
1 - P(Z<3)
From the table
P(Z < -3) = 0.0013
The probability of the runners have times less than 14.4 secs is 0.0013 = 0.13%
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Answer:
He Melanie , use SOH CAH TOA to remember the trig functions
Step-by-step explanation:
for 14 they hyp = 22 and we know one angle of 45°, we also know that the triangle has a right angle or 90° and by inspection we can tell that the other angle is also going to be 45° so we know X and Y will be the same length, is why this is a good observation.
Use one of the trig functions with H in it b/c you know Hyp is 22, so,
SOH = Sin(Θ)= Opp / Hyp
Sin(45) = Opp / 22
Sin(45) * 22 = Opp
/ 2 * 22 = opp
11* = opp is the exact answer, if you would like some decimal places, it's 7.7781 units, both X and Y
for 15 we can use SOH again for the bigger triangle. we know the Hyp is 24 and the angle is 30°
Sin(30) = Opp / 24
Sin(30) *24 = Opp
12 = Opp ( Because I know Sin(30) = 1/2 )
Opp is the upright between the two triangles
Use CAH Cos(Θ) = Adj / Hyp
Cos(30) = Adj / 24
Cos(30) * 24 = Adj
/2 *24 =Adj
12 = Adj
Z = 12 or if you want some decimals 20.7846
Becasue the smaller triangle is also a 45° right triangle we know that the upright and side Y are the same lengths
then
Y = 12
You could use SOH or CAH to find the Hyp but, lets just resort to Pythagoras, and use his formula to find Hyp
Hyp =
Hyp =
hyp = 16.97
X = 16.97
:)
Answers: A , B , and D are correct.
________________________________________________________
The following statements are true and correct:
____________________________________________________
[A]: y is a function of x .
____________________________________________________
[B]: The graph of the relationship is a line.
____________________________________________________
[D]: When the input is -2, the output is 3.
____________________________________________________
Note:
____________________________________________________
Choice: [C]: "When the input is -3, the output is 4 ." → is INCORRECT.
Note: When the input is -3, the output is "4 <span>⅓";
that is, when x = -3, y = 4 </span>⅓ .
_____________________________________________________
Choice: [E]: "The y-intercept of the relationship is: (0,1)." → is incorrect.
Note: The y-intercept refers to the value of "y" where the line crosses the "x" axis. From the equation; and form the graph, we see that the y-intercept is: "⅓" ; or, "(0, ⅓)" .
<span>________________________________________________________
</span>Here is the graph of the equation:
____________________________________________
y =
;
_____________________________________________
________________________________________________________
The following statements are true and correct:
____________________________________________________
[A]: y is a function of x .
____________________________________________________
[B]: The graph of the relationship is a line.
____________________________________________________
[D]: When the input is -2, the output is 3.
____________________________________________________
Note:
____________________________________________________
Choice: [C]: "When the input is -3, the output is 4 ." → is INCORRECT.
Note: When the input is -3, the output is "4 <span>⅓";
that is, when x = -3, y = 4 </span>⅓ .
_____________________________________________________
Choice: [E]: "The y-intercept of the relationship is: (0,1)." → is incorrect.
Note: The y-intercept refers to the value of "y" where the line crosses the "x" axis. From the equation; and form the graph, we see that the y-intercept is: "⅓" ; or, "(0, ⅓)" .
<span>________________________________________________________
</span>Here is the graph of the equation:
____________________________________________
y =
_____________________________________________