Question

A population is normally distributed with

μ=200

and

σ=10.

a.	Find the probability that a value randomly selected from this population will have a value greater than 210.
b.	Find the probability that a value randomly selected from this population will have a value less than 190.
c.	Find the probability that a value randomly selected from this population will have a value between 190 and 210.

a. ​P(x>210​)=

​(Round to four decimal places as​ needed.)

b. ​P(x<190​)=

​(Round to four decimal places as​ needed.)

c. P(190<x<210​)=

​(Round to four decimal places as​ needed.)

Answer 1

For normal distribution,

P(X<x) = P(Z <X-μ/σ)

a) p(X>210) = p( z > 210 - 200 / 10)

= p( z > 1)

= 1-p (z < 1)

= 1 - 0.84134

=0.15866

probability that a value randomly selected from this population will have a value greater than 210 = 0.15866

b)

p(X< 90) = p( z <190 - 200 / 10)

= p( z<-1)

= 1- p( z< 1) =

1 - 0.84134

= 0.1587

probability that a value randomly selected from

this population will have a value less than 190 = 0.1587

c)

p( 190 < X < 210) = P(X< 210) - P( X < 190)

= P (Z < 210 - 200 / 10) - P(Z< 190 - 200 / 10)

= P(Z < 1) - p( z <-1)

= p(z< 1) - (1-p (z<1 ))

= 0.84134 - ( 1-0.84134)

= 0.68268

probability that a value randomly selected from this population will have a value between 190 and 210 = 0.68268

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