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Chapter 5: Q. 5.15 (page 213)

If Xis a normal random variable with parameters 渭=10and 蟽2=36, compute

(a)role="math" localid="1646719347104" PX>5

(b)role="math" localid="1646719357568" P4<X<16

(c)role="math" localid="1646719367217" PX<8

(d)PX<20

(e)PX>16

Short Answer

Expert verified

The required answers are:

(a)PX>5=0.7977

(b)P4<X<16=0.6826

(c)role="math" localid="1646720604668" Px<8=0.3695

(d)PX<20=0.9522

(e)PX>16=0.1587

Step by step solution

01

Part (a) Step 1. Given information.

Here, it is given that:

渭=10蟽2=36鈭�蟽=36=6

02

Part (a) Step 2. Compute P(X>5).

P(X>5)=PX-渭蟽>5-106=Pz>5-106=1-Pz鈮�5-106=1-Pz鈮�0.8333=1-0.2023鈭�P(X>5)=0.7977

03

Part (b) Step 1. Compute P4<X<16.

P(4<X<16)=P4-106<X-渭蟽<16-106=P-1<z<1=P(z<1)-P(z<-1)=0.8413-0.1587鈭�P(4<X<16)=0.6826

04

Part (c) Step 1. Compute P(X<8).

P(X<8)=PX-渭蟽<8-106=Pz<-0.3333鈭�P(X<8)=0.3695

05

Part (d) Step 1. Compute PX<20.

P(X<20)=PX-渭蟽<20-106=Pz<1.6667鈭�P(X<20)=0.9522

06

Part (e) Step 1. Compute PX>16.

P(X>16)=PX-渭蟽>16-106=Pz>1=1-Pz鈮�1=1-0.8413鈭�P(X>16)=0.1587

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