Let X be the national sat score. X follows normal distribution with mean μ =1028, standard deviation σ = 92
The 90th percentile score is nothing but the x value for which area below x is 90%.
To find 90th percentile we will find find z score such that probability below z is 0.9
P(Z <z) = 0.9
Using excel function to find z score corresponding to probability 0.9 is
z = NORM.S.INV(0.9) = 1.28
z =1.28
Now convert z score into x value using the formula
x = z *σ + μ
x = 1.28 * 92 + 1028
x = 1145.76
The 90th percentile score value is 1145.76
The probability that randomly selected score exceeds 1200 is
P(X > 1200)
Z score corresponding to x=1200 is
z = 
z = 
z = 1.8695 ~ 1.87
P(Z > 1.87 ) = 1 - P(Z < 1.87)
Using z-score table to find probability z < 1.87
P(Z < 1.87) = 0.9693
P(Z > 1.87) = 1 - 0.9693
P(Z > 1.87) = 0.0307
The probability that a randomly selected score exceeds 1200 is 0.0307
Answer:
Step-by-step explanation:
Given:
Txo six-sided dice are rolled.
Total number of outcomes n(S) = 36
We need to find the probability that the sum is not equal to 5 p(Not 5).
Solution:
Using probability formula.
----------------(1)
Where:
n(E) is the number of outcomes favourable to E.
n(S) is the total number of equally likely outcomes.
The sum of two six-sided dice roll outcome is equal to 5 as.
Outcome as 5: {(1,4), (2,3), (3,2), (4,1)}
So, the total favourable events n(E) = 4
Now, we substitute n(E) and n(s) in equation 1.
Using formula.
Now we substitute p(5) in above equation.
Therefore, the sum of two six-sided dice roll outcome is not equal to 5.
We'll have to add up all the fractions.
First, find the LCM of the denominators.
To do this, we'll use the listing method.
4: 4, 8, 12, 16, 20, 24, 28, 32, 36, all the way to 140.
5: 5, 10, 15, 20, 25, 30, 35, all the way to 140.
7: 7, 14, 21, 28, 35, 42, 49, all the way to 140.
So, 140 is the Least Common Multiple.
Multiply the numerator of 1 as many times you multiplied 4 to get to 140, which is 35.
1 x 35 = 35.
Multiply the numerator of 2 as many times you multiplied 5 to get to 140, which is 28.
2 x 28 = 56
Multiply the numerator of 3 as many times you multiplied 7 to get to 140, which is 20.
3 x 20 = 60.
So: 35/140 + 56/140 + 60/140
=35/140 + 116/140
=151/140
=1 11/140
So, the swimmer swam 1 and 11/140th of a mile.
Answer:
the answer is #4 because the quadrant 1 starts at the top right and it goes counterclockwise
Step-by-step explanation:
