Answer:
d=9
Step-by-step explanation:
Answer:
a) 0.1003
b) 35.26
c) 21.92
d) Middle 80% smallest 10% and largest 10% = 20.02 and 39.98
Step-by-step explanation:
Given that: mean ц = 30 , standard deviation δ = 7.8
a) P(x ≤ 20)
= P [ (x - ц ) / δ ≤ ( 20 -30) / 7.8 ]
= P(z ≤ -1.28)
= 0.1003
probability = 0.1003
b) 75th percentile
P(Z < z) = 0.75
z = 0.674
Using z-score formula
x = z * δ + ц
x = 0.674 * 7.8 + 30
x = 35.26
c) 15th percentile
P(Z < z) = 0.15
z = -1.036
Using z-score formula
x = z * δ + ц
x = (-1.036) * 7.8 + 30
x = 21.92
d) Middle 80%
P(-z ≤ Z ≤ z) = 0.80
P(Z ≤ z) - P(Z ≤ -z) = 0.80
2P(Z ≤ z) - 1 = 0.80
2P(Z ≤ z) = 1 + 0.80 = 1.80
P(Z ≤ z) = 1.80 / 2 = 0.90
P(Z ≤ ± 1.28) = 0.90
z = -1.28, + 1.28
x = z * δ + ц
x = (-1.28) * 7.8 + 30
x = 20.02
x = z * δ + ц
x = 1.28 * 7.8 + 30
x = 39.98
Middle 80% two values = 20.02 and 39.98
smallest 10%
P(Z < z) = 0.10
z = -1.28
Using z-score formula
x = z * δ + ц
x = ( -1.28) * 7.8 + 30
x = 20.02
largest 10%
P(Z > z ) = 0.10
1 - P(z < z) = 0.10
P(z < z) = 1 - 0.10 = 0.90
z = 1.28
Using z-score formula
x = z * δ + ц
x = (1.28) * 7.8 + 30
x = 39.98
Answer:
dab= 43 degrees
Step-by-step explanation:
this is because of a property in geometry (I dont remember the name) that says when your lines are parallel to each other with that line through the center like that, the degrees cross
So he spends $12.50 a week since there is 5 days of school a week. He can spend $1.50 a day since there is 7.50 left from the week. So he can get a hamburger and use 1.50 every week and reach his budget of $20