# Normal Distribution 題目

2.Consider a standard normal variable Z. Find c such that

a)P(Z &lt; c) = 0.8

b)P(Z &lt; c) = 0.27

c)P(0 &lt; Z &lt; c) = 0.311

find 0.8 from the table and c = 0.8416

find 0.8 from the table and c = 0.8416

0.8416係起1.0 個行

2.a) 0.84b) –0.61c) 0.88

### 2 個解答

• 最佳解答

2.

the left hand side column and top row of the normal distribution table is the Z value

the value inside the table represent the probability

a)

since P(Z &lt; c) is more than 0.5

it should be consider the inverse part

P(Z &lt; c) = 0.8

1 - P(Z &gt; c) = 0.8

P(Z &gt; c) = 0.2

c = 0.84

find the probability about 0.2 from the table, the Z value of this probability is 0.84

b)

P(Z &lt; c) = 0.27

c = -0.61

find the probability about 0.27 from the table, the Z value of this probability is 0.61

since P(Z &lt; c) is less than 0.5, the Z value is negative

c)

P(0 &lt; Z &lt; c) = 0.311

0.5 - P(Z &gt; c) = 0.311

P(Z &gt; c) = 0.189

c = 0.88

• look at the inverse normal function table,

a)inverse of [Q] (p) = z

find 0.8 from the table and c = 0.8416

b)invese of p(0.27) = -p(0.73) c = -0.6128

i am not sure about the third one, should be something like 0.5 - -p(0.689)

=0.5 - 0.4930