Question

In: Statistics and Probability

Given a normal distribution with u = 70 and o= 20, what is the probability that...

Given a normal distribution with u = 70 and o= 20, what is the probability that

X>110
X<10
X < 70 or x> 130
Between what two x values (symmetrically distributed around the mean) are 70% of the values

Expert Solution

Given,

= 70 , = 20

We convert this to standard normal as

P(X < x) = P( Z < x - / )

a)

P(X > 110) = P(Z > (110 - 70) / 20 )

= P(Z > 2)

= 0.0228

b)

P(X < 10) = P(Z < 10 - 70 / 20)

= P(Z < -3)

= 0.0013

c)

P(X < 70 OR X > 130) = 1 - P(70 < X < 130)

= 1 - [ P(X < 130) - P(X < 70) ]

= 1 - [ P(Z < 130 - 70 / 20) - P(Z < 70 - 70 / 20) ]

= 1 - [ P(Z < 3) - P(Z < 0) ]

= 1 - [ 0.9987 - 0.5]

= 0.5013

d)

= 1 - 0.70 = 0.30

Z/2 = Z_0.15 = 1.0364

70% of the values lies between

Z *

= 70 1.0364 * 20

70 - 1.0364 * 20 and 70 + 1.0364 * 20

49.27 and 90.73

orchestra answered 1 year ago

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