Question

If

X

X

represents a random variable coming from a normal distribution with mean 5 and if

P

(

X

>

6.7

)

=

0.34

P

(

X

>

6.7

)

=

0.34

, then

P

(

5

<

X

<

6.7

)

=

0.16

P

(

5

<

X

<

6.7

)

=

0.16

.

Answer 1

Let X. Normal with mean 5. P(x > 6.7) = 0.34 Now, PC 5 < X < 6.7) = P(X<6.7) - P(X<5) Here E(x) = 5 4 X is symmetric about mean 5 P(X<5) = P(x>5 -0.5 = & P(x > 6.7) = 0.34 I-P(X>6.7) = P(X56.7) = 1-0-34 = 0.66 P(5< X < 6.7) = 0.66 -0.5 P(5< X < 6.7) = 0.16