Answer:
Step-by-step explanation:
The formula for normal distribution is
z = (x - µ)/σ
a) P(5.7 ≤ X ≤ 16.2)
For x = 5.7,
z = (5.7 - 10.1)/3.4 = - 1.3
The corresponding probability from the normal distribution table is 0.0968
For x = 16.2,
z = (16.2 - 10.1)/3.4 = 1.8
The corresponding probability from the normal distribution table is
0.9641
Therefore,
P(5.7 ≤ X ≤ 16.2) = 0.9641 - 0.0968 =
0.8673
b) P(5.6 ≤ X ≤ 15.6)
For x = 5.6,
z = (5.6 - 10.1)/3.4 = - 1.32
The corresponding probability from the normal distribution table is 0.09342
For x = 15.6
z = (15.6 - 10.1)/3.4 = 1.62
The corresponding probability from the normal distribution table is
0.9474
Therefore,
P(5.6 ≤ X ≤ 15.6) = 0.9474 - 0.09342 = 0.85398
c) P(11.5 ≤ X ≤ 14.1)
For x = 11.5,
z = (11.5 - 10.1)/3.4 = 0.41
The corresponding probability from the normal distribution table is 0.6591
For x = 14.1
z = (14.1 - 10.1)/3.4 = 1.18
The corresponding probability from the normal distribution table is
0.881
Therefore,
P(11.5 ≤ X ≤ 14.1) = 0.881 - 0.6591 = 0.2219
d) P(X ≥ 10.7) = 1 - P(X ≤ 10.7)
For x = 10.7
z = (10.7 - 10.1)/3.4 = 0.18
The corresponding probability from the normal distribution table is
0.5714
Therefore,
P(X ≥ 10.7) = 1 - 0.5714 = 0.4286
e) P(X ≤ 14.4)
For x = 14.4
z = (14.4 - 10.1)/3.4 = 1.26
The corresponding probability from the normal distribution table is
0.9131
Therefore
P(X ≤ 14.4) = 0.9131
