5.29 Find a value zo of the standard normal random variable z such that a. P(z b
ID: 3052564 • Letter: 5
Question
5.29 Find a value zo of the standard normal random variable z such that a. P(z b. /"(z zo) =.05 zo) .025 d. /"(z zo) .10 = .1() e, P(z > zo) Suppose the random variable x is best described by a nor- mal distribution with -25 and -5. Find the z-score that corresponds to each of the following x values: a. x 25 b. x 30 c. x=37.5 d, x = 10 e. x = 50 f. x 32 5.30 5.31 Suppose x is a normally distributed random variable with = 11 and = 2. Find each of the following: NW a. P(10 s x s 12) c. P(13 s s 16) d. P(7.8 s x s 12.6) e. P(x 13.24) f. P(x z 7.62) 5.32 Suppose x is a normally distributed random variable with = 30 and = 8, Find a value xo of the random variable x such that b. P(x xo) = .10 d, P(x > xo) = .95Explanation / Answer
Result:
5.29).
a). z=1.645
b). z=1.96
c).z= -1.96
d). 1.282
e). 1.282
5.30)
x
z
25
0
30
1
37.5
2.5
10
-3
50
5
32
1.4
5.31).
a).
Probability for a Range
From X Value
10
To X Value
12
Z Value for 10
-0.5
Z Value for 12
0.5
P(X<=10)
0.3085
P(X<=12)
0.6915
P(10<=X<=12)
0.3829
P=0.3829
b).
Probability for a Range
From X Value
6
To X Value
10
Z Value for 6
-2.5
Z Value for 10
-0.5
P(X<=6)
0.0062
P(X<=10)
0.3085
P(6<=X<=10)
0.3023
c).
Probability for a Range
From X Value
13
To X Value
16
Z Value for 13
1
Z Value for 16
2.5
P(X<=13)
0.8413
P(X<=16)
0.9938
P(13<=X<=16)
0.1524
d).
Probability for a Range
From X Value
7.8
To X Value
12.6
Z Value for 7.8
-1.6
Z Value for 12.6
0.8
P(X<=7.8)
0.0548
P(X<=12.6)
0.7881
P(7.8<=X<=12.6)
0.7333
e).
Probability for X >
X Value
13.24
Z Value
1.12
P(X>13.24)
0.1314
f).
Probability for X >
X Value
7.62
Z Value
-1.69
P(X>7.62)
0.9545
x
z
25
0
30
1
37.5
2.5
10
-3
50
5
32
1.4
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